Av(21354, 21453, 21543, 31254, 31452, 31542, 41253, 41352)
Counting Sequence
1, 1, 2, 6, 24, 112, 568, 3035, 16838, 96189, 562676, 3356916, 20362850, 125287692, 780398094, ...
Implicit Equation for the Generating Function
\(\displaystyle 16 x^{6} \left(3 x -2\right) F \left(x
\right)^{5}-8 x^{4} \left(14 x^{3}-40 x^{2}+53 x -22\right) F \left(x
\right)^{4}+4 x^{2} \left(26 x^{5}-118 x^{4}+101 x^{3}+94 x^{2}-83 x +2\right) F \left(x
\right)^{3}-x \left(48 x^{6}-276 x^{5}+106 x^{4}+644 x^{3}-212 x^{2}-163 x +10\right) F \left(x
\right)^{2}+\left(11 x^{7}-72 x^{6}+15 x^{5}+296 x^{4}+77 x^{3}-188 x^{2}-11 x +2\right) F \! \left(x \right)-x^{7}+7 x^{6}-3 x^{5}-42 x^{4}-59 x^{3}+44 x^{2}+19 x -2 = 0\)
Recurrence
\(\displaystyle a(0) = 1\)
\(\displaystyle a(1) = 1\)
\(\displaystyle a(2) = 2\)
\(\displaystyle a(3) = 6\)
\(\displaystyle a(4) = 24\)
\(\displaystyle a(5) = 112\)
\(\displaystyle a(6) = 568\)
\(\displaystyle a(7) = 3035\)
\(\displaystyle a(8) = 16838\)
\(\displaystyle a(9) = 96189\)
\(\displaystyle a(10) = 562676\)
\(\displaystyle a(11) = 3356916\)
\(\displaystyle a(12) = 20362850\)
\(\displaystyle a(13) = 125287692\)
\(\displaystyle a(14) = 780398094\)
\(\displaystyle a(15) = 4913441262\)
\(\displaystyle a(16) = 31229240680\)
\(\displaystyle a(17) = 200161740988\)
\(\displaystyle a(18) = 1292576829062\)
\(\displaystyle a(19) = 8403454805199\)
\(\displaystyle a(20) = 54967211523736\)
\(\displaystyle a(21) = 361535419832333\)
\(\displaystyle a(22) = 2389947199755618\)
\(\displaystyle a(23) = 15872001924202212\)
\(\displaystyle a(24) = 105856865458351580\)
\(\displaystyle a(25) = 708772922521008784\)
\(\displaystyle a(26) = 4762871495418671492\)
\(\displaystyle a(27) = 32113740931587832751\)
\(\displaystyle a(28) = 217205931109269779570\)
\(\displaystyle a(29) = 1473397399954662005575\)
\(\displaystyle a(30) = 10021971313320552266852\)
\(\displaystyle a(31) = 68343439404117254465092\)
\(\displaystyle a{\left(n + 32 \right)} = \frac{486 n \left(2 n + 1\right) \left(4 n + 3\right) \left(4 n + 5\right) a{\left(n \right)}}{137 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{\left(187799 n + 5652356\right) a{\left(n + 31 \right)}}{4795 \left(n + 34\right)} - \frac{\left(11857573 n^{2} + 701775051 n + 10380571266\right) a{\left(n + 30 \right)}}{19180 \left(n + 33\right) \left(n + 34\right)} + \frac{\left(41286048 n^{3} + 3599516147 n^{2} + 104555141623 n + 1011813233022\right) a{\left(n + 29 \right)}}{9590 \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{27 \left(9842 n^{4} + 69690 n^{3} + 176140 n^{2} + 182490 n + 65583\right) a{\left(n + 1 \right)}}{685 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{9 \left(9927160 n^{4} + 100105540 n^{3} + 378144902 n^{2} + 634907354 n + 399967491\right) a{\left(n + 2 \right)}}{1918 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{3 \left(137195804 n^{4} + 5889775120 n^{3} + 51832915870 n^{2} + 167359634435 n + 183315722331\right) a{\left(n + 3 \right)}}{19180 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{\left(298397903 n^{4} + 34856043030 n^{3} + 1529721987325 n^{2} + 29895485662590 n + 219525644715792\right) a{\left(n + 28 \right)}}{76720 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{3 \left(20272371517 n^{4} + 303008850210 n^{3} + 1568687135000 n^{2} + 3106616534010 n + 1511089183668\right) a{\left(n + 4 \right)}}{19180 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} - \frac{\left(26618997429 n^{4} + 2947551130360 n^{3} + 122398972740125 n^{2} + 2259141023951330 n + 15638267192350456\right) a{\left(n + 27 \right)}}{76720 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} - \frac{3 \left(97881818833 n^{4} + 1083961603645 n^{3} - 807917955815 n^{2} - 41877891298315 n - 115195565564978\right) a{\left(n + 5 \right)}}{38360 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{\left(467173192609 n^{4} + 23773802377110 n^{3} + 116671112633175 n^{2} - 9447577388591230 n - 120143129964668264\right) a{\left(n + 24 \right)}}{306880 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{\left(985676669069 n^{4} + 105102141025710 n^{3} + 4202865683437635 n^{2} + 74703767191881170 n + 498008922982644936\right) a{\left(n + 26 \right)}}{306880 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} - \frac{\left(2125967030913 n^{4} + 217491644300685 n^{3} + 8346641978382150 n^{2} + 142426417538856880 n + 911873373949140752\right) a{\left(n + 25 \right)}}{153440 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} - \frac{\left(24608635556546 n^{4} + 689164507449490 n^{3} + 7211646089705545 n^{2} + 33418662141613685 n + 57865858692346584\right) a{\left(n + 6 \right)}}{76720 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{\left(43042866411828 n^{4} + 1334987646612023 n^{3} + 15488975107198161 n^{2} + 79680008978016574 n + 153355371033688464\right) a{\left(n + 7 \right)}}{15344 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{\left(62356958589842 n^{4} + 6002622431234025 n^{3} + 216422398002057725 n^{2} + 3463655719313036550 n + 20760175162395233488\right) a{\left(n + 23 \right)}}{153440 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{3 \left(348758848460025 n^{4} + 13473898490178118 n^{3} + 194862831505682819 n^{2} + 1250484224896488702 n + 3004789933576024184\right) a{\left(n + 9 \right)}}{30688 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} - \frac{\left(490569636724889 n^{4} + 45105655499918860 n^{3} + 1553997881354981455 n^{2} + 23775738003383202620 n + 136296239562585047536\right) a{\left(n + 22 \right)}}{153440 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{\left(2346444074798034 n^{4} + 206336302608874565 n^{3} + 6799577923848594635 n^{2} + 99519511107682276390 n + 545834376055576028616\right) a{\left(n + 21 \right)}}{153440 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} - \frac{\left(3630094555768813 n^{4} + 125777357395720150 n^{3} + 1630424078767905935 n^{2} + 9372203643578247590 n + 20159590975255169952\right) a{\left(n + 8 \right)}}{306880 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} - \frac{\left(8203453158346531 n^{4} + 689160780081403770 n^{3} + 21697236331187442865 n^{2} + 303409824761727229610 n + 1590028885488112522744\right) a{\left(n + 20 \right)}}{153440 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} - \frac{3 \left(8311970392479087 n^{4} + 358184160237272270 n^{3} + 5783257171901472345 n^{2} + 41471342990958094010 n + 111456312396527578408\right) a{\left(n + 10 \right)}}{306880 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{\left(16638428888515354 n^{4} + 1204485772279886699 n^{3} + 32676565381434968557 n^{2} + 393732550996529292874 n + 1777907058352732193688\right) a{\left(n + 17 \right)}}{30688 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{\left(22239237979515378 n^{4} + 1781787882772912905 n^{3} + 53500321880765244105 n^{2} + 713516272442085562550 n + 3566225797514236108752\right) a{\left(n + 19 \right)}}{153440 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} - \frac{\left(23977381979274061 n^{4} + 1828285231880450865 n^{3} + 52245026510179543165 n^{2} + 663114687876004329325 n + 3154180897223740271764\right) a{\left(n + 18 \right)}}{76720 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} - \frac{\left(24037746699829213 n^{4} + 1459448697300486472 n^{3} + 33202487660034853965 n^{2} + 335450145595956207498 n + 1269923832106391425216\right) a{\left(n + 14 \right)}}{30688 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{\left(27113292379320764 n^{4} + 1296511990275328095 n^{3} + 23237801894900970545 n^{2} + 185035479482980977570 n + 552329845864650211136\right) a{\left(n + 11 \right)}}{153440 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} - \frac{\left(53099079041637489 n^{4} + 2781830356304083870 n^{3} + 54618207058495915195 n^{2} + 476327067725085511030 n + 1556891750600358316056\right) a{\left(n + 12 \right)}}{153440 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} - \frac{\left(58283144035263622 n^{4} + 3994225567747406830 n^{3} + 102576435178103339765 n^{2} + 1169967660787598845565 n + 5000634353811311178118\right) a{\left(n + 16 \right)}}{76720 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{\left(88358984246516282 n^{4} + 5006537159581866375 n^{3} + 106297591010649121885 n^{2} + 1002305540338833025970 n + 3541494443405221672448\right) a{\left(n + 13 \right)}}{153440 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{\left(131862965169749994 n^{4} + 8525006286182077605 n^{3} + 206523326604132055205 n^{2} + 2221944349090094873850 n + 8957813130461353374296\right) a{\left(n + 15 \right)}}{153440 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)}, \quad n \geq 32\)
\(\displaystyle a(1) = 1\)
\(\displaystyle a(2) = 2\)
\(\displaystyle a(3) = 6\)
\(\displaystyle a(4) = 24\)
\(\displaystyle a(5) = 112\)
\(\displaystyle a(6) = 568\)
\(\displaystyle a(7) = 3035\)
\(\displaystyle a(8) = 16838\)
\(\displaystyle a(9) = 96189\)
\(\displaystyle a(10) = 562676\)
\(\displaystyle a(11) = 3356916\)
\(\displaystyle a(12) = 20362850\)
\(\displaystyle a(13) = 125287692\)
\(\displaystyle a(14) = 780398094\)
\(\displaystyle a(15) = 4913441262\)
\(\displaystyle a(16) = 31229240680\)
\(\displaystyle a(17) = 200161740988\)
\(\displaystyle a(18) = 1292576829062\)
\(\displaystyle a(19) = 8403454805199\)
\(\displaystyle a(20) = 54967211523736\)
\(\displaystyle a(21) = 361535419832333\)
\(\displaystyle a(22) = 2389947199755618\)
\(\displaystyle a(23) = 15872001924202212\)
\(\displaystyle a(24) = 105856865458351580\)
\(\displaystyle a(25) = 708772922521008784\)
\(\displaystyle a(26) = 4762871495418671492\)
\(\displaystyle a(27) = 32113740931587832751\)
\(\displaystyle a(28) = 217205931109269779570\)
\(\displaystyle a(29) = 1473397399954662005575\)
\(\displaystyle a(30) = 10021971313320552266852\)
\(\displaystyle a(31) = 68343439404117254465092\)
\(\displaystyle a{\left(n + 32 \right)} = \frac{486 n \left(2 n + 1\right) \left(4 n + 3\right) \left(4 n + 5\right) a{\left(n \right)}}{137 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{\left(187799 n + 5652356\right) a{\left(n + 31 \right)}}{4795 \left(n + 34\right)} - \frac{\left(11857573 n^{2} + 701775051 n + 10380571266\right) a{\left(n + 30 \right)}}{19180 \left(n + 33\right) \left(n + 34\right)} + \frac{\left(41286048 n^{3} + 3599516147 n^{2} + 104555141623 n + 1011813233022\right) a{\left(n + 29 \right)}}{9590 \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{27 \left(9842 n^{4} + 69690 n^{3} + 176140 n^{2} + 182490 n + 65583\right) a{\left(n + 1 \right)}}{685 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{9 \left(9927160 n^{4} + 100105540 n^{3} + 378144902 n^{2} + 634907354 n + 399967491\right) a{\left(n + 2 \right)}}{1918 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{3 \left(137195804 n^{4} + 5889775120 n^{3} + 51832915870 n^{2} + 167359634435 n + 183315722331\right) a{\left(n + 3 \right)}}{19180 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{\left(298397903 n^{4} + 34856043030 n^{3} + 1529721987325 n^{2} + 29895485662590 n + 219525644715792\right) a{\left(n + 28 \right)}}{76720 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{3 \left(20272371517 n^{4} + 303008850210 n^{3} + 1568687135000 n^{2} + 3106616534010 n + 1511089183668\right) a{\left(n + 4 \right)}}{19180 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} - \frac{\left(26618997429 n^{4} + 2947551130360 n^{3} + 122398972740125 n^{2} + 2259141023951330 n + 15638267192350456\right) a{\left(n + 27 \right)}}{76720 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} - \frac{3 \left(97881818833 n^{4} + 1083961603645 n^{3} - 807917955815 n^{2} - 41877891298315 n - 115195565564978\right) a{\left(n + 5 \right)}}{38360 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{\left(467173192609 n^{4} + 23773802377110 n^{3} + 116671112633175 n^{2} - 9447577388591230 n - 120143129964668264\right) a{\left(n + 24 \right)}}{306880 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{\left(985676669069 n^{4} + 105102141025710 n^{3} + 4202865683437635 n^{2} + 74703767191881170 n + 498008922982644936\right) a{\left(n + 26 \right)}}{306880 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} - \frac{\left(2125967030913 n^{4} + 217491644300685 n^{3} + 8346641978382150 n^{2} + 142426417538856880 n + 911873373949140752\right) a{\left(n + 25 \right)}}{153440 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} - \frac{\left(24608635556546 n^{4} + 689164507449490 n^{3} + 7211646089705545 n^{2} + 33418662141613685 n + 57865858692346584\right) a{\left(n + 6 \right)}}{76720 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{\left(43042866411828 n^{4} + 1334987646612023 n^{3} + 15488975107198161 n^{2} + 79680008978016574 n + 153355371033688464\right) a{\left(n + 7 \right)}}{15344 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{\left(62356958589842 n^{4} + 6002622431234025 n^{3} + 216422398002057725 n^{2} + 3463655719313036550 n + 20760175162395233488\right) a{\left(n + 23 \right)}}{153440 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{3 \left(348758848460025 n^{4} + 13473898490178118 n^{3} + 194862831505682819 n^{2} + 1250484224896488702 n + 3004789933576024184\right) a{\left(n + 9 \right)}}{30688 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} - \frac{\left(490569636724889 n^{4} + 45105655499918860 n^{3} + 1553997881354981455 n^{2} + 23775738003383202620 n + 136296239562585047536\right) a{\left(n + 22 \right)}}{153440 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{\left(2346444074798034 n^{4} + 206336302608874565 n^{3} + 6799577923848594635 n^{2} + 99519511107682276390 n + 545834376055576028616\right) a{\left(n + 21 \right)}}{153440 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} - \frac{\left(3630094555768813 n^{4} + 125777357395720150 n^{3} + 1630424078767905935 n^{2} + 9372203643578247590 n + 20159590975255169952\right) a{\left(n + 8 \right)}}{306880 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} - \frac{\left(8203453158346531 n^{4} + 689160780081403770 n^{3} + 21697236331187442865 n^{2} + 303409824761727229610 n + 1590028885488112522744\right) a{\left(n + 20 \right)}}{153440 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} - \frac{3 \left(8311970392479087 n^{4} + 358184160237272270 n^{3} + 5783257171901472345 n^{2} + 41471342990958094010 n + 111456312396527578408\right) a{\left(n + 10 \right)}}{306880 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{\left(16638428888515354 n^{4} + 1204485772279886699 n^{3} + 32676565381434968557 n^{2} + 393732550996529292874 n + 1777907058352732193688\right) a{\left(n + 17 \right)}}{30688 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{\left(22239237979515378 n^{4} + 1781787882772912905 n^{3} + 53500321880765244105 n^{2} + 713516272442085562550 n + 3566225797514236108752\right) a{\left(n + 19 \right)}}{153440 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} - \frac{\left(23977381979274061 n^{4} + 1828285231880450865 n^{3} + 52245026510179543165 n^{2} + 663114687876004329325 n + 3154180897223740271764\right) a{\left(n + 18 \right)}}{76720 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} - \frac{\left(24037746699829213 n^{4} + 1459448697300486472 n^{3} + 33202487660034853965 n^{2} + 335450145595956207498 n + 1269923832106391425216\right) a{\left(n + 14 \right)}}{30688 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{\left(27113292379320764 n^{4} + 1296511990275328095 n^{3} + 23237801894900970545 n^{2} + 185035479482980977570 n + 552329845864650211136\right) a{\left(n + 11 \right)}}{153440 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} - \frac{\left(53099079041637489 n^{4} + 2781830356304083870 n^{3} + 54618207058495915195 n^{2} + 476327067725085511030 n + 1556891750600358316056\right) a{\left(n + 12 \right)}}{153440 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} - \frac{\left(58283144035263622 n^{4} + 3994225567747406830 n^{3} + 102576435178103339765 n^{2} + 1169967660787598845565 n + 5000634353811311178118\right) a{\left(n + 16 \right)}}{76720 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{\left(88358984246516282 n^{4} + 5006537159581866375 n^{3} + 106297591010649121885 n^{2} + 1002305540338833025970 n + 3541494443405221672448\right) a{\left(n + 13 \right)}}{153440 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)} + \frac{\left(131862965169749994 n^{4} + 8525006286182077605 n^{3} + 206523326604132055205 n^{2} + 2221944349090094873850 n + 8957813130461353374296\right) a{\left(n + 15 \right)}}{153440 \left(n + 31\right) \left(n + 32\right) \left(n + 33\right) \left(n + 34\right)}, \quad n \geq 32\)
This specification was found using the strategy pack "Point Placements Tracked Fusion Tracked Component Fusion Symmetries" and has 162 rules.
Finding the specification took 59466 seconds.
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\(\begin{align*}
F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{1}\! \left(x \right) &= 1\\
F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{30}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{30}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{155}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{11}\! \left(x \right) F_{30}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x , 1\right)\\
F_{12}\! \left(x , y\right) &= F_{13}\! \left(x , y\right)+F_{153}\! \left(x , y\right)\\
F_{14}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{30}\! \left(x \right)\\
F_{14}\! \left(x , y\right) &= F_{15}\! \left(x , y\right)\\
F_{16}\! \left(x , y\right) &= F_{15}\! \left(x , y\right)+F_{23}\! \left(x , y\right)\\
F_{17}\! \left(x , y\right) &= F_{151}\! \left(x , y\right)+F_{16}\! \left(x , y\right)\\
F_{18}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{27}\! \left(x , y\right)\\
F_{18}\! \left(x , y\right) &= F_{19}\! \left(x , y\right)\\
F_{19}\! \left(x , y\right) &= F_{20}\! \left(x , y\right)\\
F_{20}\! \left(x , y\right) &= F_{21}\! \left(x , y\right) F_{27}\! \left(x , y\right)\\
F_{21}\! \left(x , y\right) &= F_{22}\! \left(x , y\right)+F_{33}\! \left(x , y\right)\\
F_{22}\! \left(x , y\right) &= F_{23}\! \left(x , y\right)+F_{31}\! \left(x , y\right)\\
F_{23}\! \left(x , y\right) &= F_{24}\! \left(x , y\right)+F_{28}\! \left(x , y\right)\\
F_{24}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{25}\! \left(x , y\right)\\
F_{25}\! \left(x , y\right) &= F_{26}\! \left(x , y\right)\\
F_{26}\! \left(x , y\right) &= F_{24}\! \left(x , y\right) F_{27}\! \left(x , y\right)\\
F_{27}\! \left(x , y\right) &= y x\\
F_{28}\! \left(x , y\right) &= F_{29}\! \left(x , y\right)\\
F_{29}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{30}\! \left(x \right)\\
F_{30}\! \left(x \right) &= x\\
F_{31}\! \left(x , y\right) &= y F_{32}\! \left(x , y\right)\\
F_{32}\! \left(x , y\right) &= F_{29}\! \left(x , y\right)\\
F_{33}\! \left(x , y\right) &= F_{34}\! \left(x , y\right)\\
F_{34}\! \left(x , y\right) &= F_{30}\! \left(x \right) F_{35}\! \left(x , y\right)\\
F_{36}\! \left(x , y\right) &= F_{27}\! \left(x , y\right) F_{35}\! \left(x , y\right)\\
F_{36}\! \left(x , y\right) &= F_{37}\! \left(x , y\right)\\
F_{37}\! \left(x , y\right) &= F_{19}\! \left(x , y\right)+F_{38}\! \left(x , y\right)\\
F_{38}\! \left(x , y\right) &= F_{39}\! \left(x , y\right)\\
F_{39}\! \left(x , y\right) &= F_{30}\! \left(x \right) F_{40}\! \left(x , y\right)\\
F_{40}\! \left(x , y\right) &= F_{144}\! \left(x , y\right)+F_{41}\! \left(x , y\right)\\
F_{41}\! \left(x , y\right) &= F_{42}\! \left(x , y\right)+F_{43}\! \left(x , y\right)\\
F_{42}\! \left(x , y\right) &= -\frac{y \left(F_{37}\! \left(x , 1\right)-F_{37}\! \left(x , y\right)\right)}{-1+y}\\
F_{44}\! \left(x , y\right) &= F_{130}\! \left(x , y\right)+F_{43}\! \left(x , y\right)\\
F_{44}\! \left(x , y\right) &= F_{45}\! \left(x , y\right)+F_{48}\! \left(x , y\right)\\
F_{45}\! \left(x , y\right) &= F_{2}\! \left(x \right) F_{46}\! \left(x , y\right)\\
F_{46}\! \left(x , y\right) &= F_{47}\! \left(x , y\right)\\
F_{47}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{27}\! \left(x , y\right)\\
F_{48}\! \left(x , y\right) &= F_{49}\! \left(x , y\right)\\
F_{49}\! \left(x , y\right) &= F_{30}\! \left(x \right) F_{50}\! \left(x , y\right)\\
F_{50}\! \left(x , y\right) &= F_{126}\! \left(x , y\right)+F_{51}\! \left(x , y\right)\\
F_{51}\! \left(x , y\right) &= -\frac{y \left(F_{52}\! \left(x , 1\right)-F_{52}\! \left(x , y\right)\right)}{-1+y}\\
F_{52}\! \left(x , y\right) &= F_{124}\! \left(x , y\right)+F_{53}\! \left(x , y\right)\\
F_{53}\! \left(x , y\right) &= F_{0}\! \left(x \right) F_{54}\! \left(x , y\right)\\
F_{55}\! \left(x , y\right) &= F_{54}\! \left(x , y\right)+F_{92}\! \left(x \right)\\
F_{55}\! \left(x , y\right) &= F_{13}\! \left(x , y\right)+F_{56}\! \left(x , y\right)\\
F_{56}\! \left(x , y\right) &= F_{57}\! \left(x , y\right)\\
F_{57}\! \left(x , y\right) &= F_{30}\! \left(x \right) F_{58}\! \left(x , y\right)\\
F_{58}\! \left(x , y\right) &= F_{59}\! \left(x , y\right)+F_{69}\! \left(x , y\right)\\
F_{59}\! \left(x , y\right) &= F_{60}\! \left(x , y\right)+F_{91}\! \left(x , y\right)\\
F_{60}\! \left(x , y\right) &= F_{61}\! \left(x , y\right)+F_{72}\! \left(x , y\right)\\
F_{61}\! \left(x , y\right) &= F_{62}\! \left(x , y\right)+F_{69}\! \left(x , y\right)\\
F_{62}\! \left(x , y\right) &= F_{63}\! \left(x , y\right)+F_{67}\! \left(x , y\right)\\
F_{63}\! \left(x , y\right) &= F_{23}\! \left(x , y\right) F_{64}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{65}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{66}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{30}\! \left(x \right) F_{64}\! \left(x \right)\\
F_{67}\! \left(x , y\right) &= F_{68}\! \left(x , y\right)\\
F_{68}\! \left(x , y\right) &= F_{30}\! \left(x \right) F_{55}\! \left(x , y\right) F_{64}\! \left(x \right)\\
F_{69}\! \left(x , y\right) &= F_{70}\! \left(x , y\right)\\
F_{70}\! \left(x , y\right) &= F_{30}\! \left(x \right) F_{59}\! \left(x , y\right) F_{71}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{64}\! \left(x \right)\\
F_{72}\! \left(x , y\right) &= F_{73}\! \left(x , y\right)\\
F_{73}\! \left(x , y\right) &= F_{30}\! \left(x \right) F_{61}\! \left(x , y\right) F_{74}\! \left(x , y\right)\\
F_{74}\! \left(x , y\right) &= F_{75}\! \left(x , y\right)+F_{76}\! \left(x , y\right)\\
F_{75}\! \left(x , y\right) &= F_{4}\! \left(x \right)+F_{46}\! \left(x , y\right)\\
F_{76}\! \left(x , y\right) &= F_{77}\! \left(x , y\right)\\
F_{77}\! \left(x , y\right) &= F_{30}\! \left(x \right) F_{78}\! \left(x , y\right)\\
F_{78}\! \left(x , y\right) &= F_{13}\! \left(x , y\right)+F_{79}\! \left(x , y\right)\\
F_{79}\! \left(x , y\right) &= F_{80}\! \left(x , y\right)\\
F_{80}\! \left(x , y\right) &= F_{27}\! \left(x , y\right) F_{81}\! \left(x , y\right)\\
F_{81}\! \left(x , y\right) &= F_{82}\! \left(x , y\right)+F_{85}\! \left(x , y\right)\\
F_{82}\! \left(x , y\right) &= F_{83}\! \left(x , y\right)+F_{89}\! \left(x , y\right)\\
F_{83}\! \left(x , y\right) &= F_{84}\! \left(x , y\right)+F_{87}\! \left(x , y\right)\\
F_{84}\! \left(x , y\right) &= F_{17}\! \left(x , y\right)+F_{85}\! \left(x , y\right)\\
F_{85}\! \left(x , y\right) &= F_{86}\! \left(x , y\right)\\
F_{86}\! \left(x , y\right) &= F_{30}\! \left(x \right) F_{71}\! \left(x \right) F_{82}\! \left(x , y\right)\\
F_{87}\! \left(x , y\right) &= F_{88}\! \left(x , y\right)\\
F_{88}\! \left(x , y\right) &= F_{30}\! \left(x \right) F_{74}\! \left(x , y\right) F_{84}\! \left(x , y\right)\\
F_{89}\! \left(x , y\right) &= F_{90}\! \left(x , y\right)\\
F_{90}\! \left(x , y\right) &= F_{24}\! \left(x , y\right) F_{30}\! \left(x \right) F_{78}\! \left(x , y\right)\\
F_{91}\! \left(x , y\right) &= F_{67}\! \left(x , y\right)\\
F_{92}\! \left(x \right) &= F_{93}\! \left(x , 1\right)\\
F_{93}\! \left(x , y\right) &= F_{94}\! \left(x \right)+F_{99}\! \left(x , y\right)\\
F_{94}\! \left(x \right) &= \frac{F_{95}\! \left(x \right)}{F_{30}\! \left(x \right)}\\
F_{95}\! \left(x \right) &= F_{96}\! \left(x \right)\\
F_{96}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{97}\! \left(x \right)\\
F_{97}\! \left(x \right) &= \frac{F_{98}\! \left(x \right)}{F_{30}\! \left(x \right)}\\
F_{98}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{99}\! \left(x , y\right) &= F_{100}\! \left(x , y\right)\\
F_{100}\! \left(x , y\right) &= F_{101}\! \left(x , y\right) F_{27}\! \left(x , y\right)\\
F_{101}\! \left(x , y\right) &= F_{102}\! \left(x , y\right)+F_{123}\! \left(x , y\right)\\
F_{102}\! \left(x , y\right) &= F_{103}\! \left(x , y\right)+F_{122}\! \left(x , y\right)\\
F_{103}\! \left(x , y\right) &= F_{104}\! \left(x , y\right)+F_{118}\! \left(x , y\right)\\
F_{104}\! \left(x , y\right) &= F_{105}\! \left(x , y\right)+F_{106}\! \left(x , y\right)\\
F_{105}\! \left(x , y\right) &= F_{24}\! \left(x , y\right) F_{97}\! \left(x \right)\\
F_{106}\! \left(x , y\right) &= F_{107}\! \left(x , y\right)\\
F_{107}\! \left(x , y\right) &= F_{102}\! \left(x , y\right) F_{108}\! \left(x , y\right) F_{30}\! \left(x \right)\\
F_{108}\! \left(x , y\right) &= F_{109}\! \left(x , y\right)\\
F_{109}\! \left(x , y\right) &= F_{110}\! \left(x , y\right)+F_{71}\! \left(x \right)\\
F_{110}\! \left(x , y\right) &= F_{111}\! \left(x , y\right)+F_{25}\! \left(x , y\right)\\
F_{111}\! \left(x , y\right) &= F_{112}\! \left(x \right)+F_{113}\! \left(x , y\right)+F_{117}\! \left(x , y\right)\\
F_{112}\! \left(x \right) &= 0\\
F_{113}\! \left(x , y\right) &= F_{114}\! \left(x , y\right) F_{27}\! \left(x , y\right)\\
F_{114}\! \left(x , y\right) &= F_{111}\! \left(x , y\right)+F_{115}\! \left(x \right)\\
F_{115}\! \left(x \right) &= F_{116}\! \left(x \right)\\
F_{116}\! \left(x \right) &= F_{30}\! \left(x \right) F_{71}\! \left(x \right)\\
F_{117}\! \left(x , y\right) &= F_{110}\! \left(x , y\right) F_{30}\! \left(x \right)\\
F_{118}\! \left(x , y\right) &= F_{119}\! \left(x , y\right)\\
F_{119}\! \left(x , y\right) &= F_{104}\! \left(x , y\right) F_{120}\! \left(x \right) F_{30}\! \left(x \right)\\
F_{120}\! \left(x \right) &= F_{121}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{5}\! \left(x \right)\\
F_{122}\! \left(x , y\right) &= F_{24}\! \left(x , y\right) F_{96}\! \left(x \right)\\
F_{123}\! \left(x , y\right) &= F_{106}\! \left(x , y\right)\\
F_{124}\! \left(x , y\right) &= F_{125}\! \left(x , y\right) F_{2}\! \left(x \right)\\
F_{13}\! \left(x , y\right) &= F_{125}\! \left(x , y\right)+F_{94}\! \left(x \right)\\
F_{126}\! \left(x , y\right) &= F_{0}\! \left(x \right) F_{127}\! \left(x , y\right)\\
F_{128}\! \left(x , y\right) &= F_{127}\! \left(x , y\right)+F_{143}\! \left(x , y\right)\\
F_{129}\! \left(x , y\right) &= F_{128}\! \left(x , y\right) F_{30}\! \left(x \right)\\
F_{129}\! \left(x , y\right) &= F_{130}\! \left(x , y\right)\\
F_{130}\! \left(x , y\right) &= F_{131}\! \left(x , y\right)\\
F_{131}\! \left(x , y\right) &= F_{132}\! \left(x , y\right) F_{27}\! \left(x , y\right)\\
F_{132}\! \left(x , y\right) &= F_{133}\! \left(x , y\right)+F_{139}\! \left(x , y\right)\\
F_{133}\! \left(x , y\right) &= -\frac{-F_{134}\! \left(x , y\right)+F_{134}\! \left(x , 1\right)}{-1+y}\\
F_{134}\! \left(x , y\right) &= F_{135}\! \left(x , y\right)\\
F_{135}\! \left(x , y\right) &= F_{136}\! \left(x , y\right) F_{27}\! \left(x , y\right)\\
F_{137}\! \left(x , y\right) &= F_{136}\! \left(x , y\right) F_{27}\! \left(x , y\right)\\
F_{137}\! \left(x , y\right) &= F_{138}\! \left(x , y\right)\\
F_{78}\! \left(x , y\right) &= F_{138}\! \left(x , y\right)+F_{93}\! \left(x , y\right)\\
F_{139}\! \left(x , y\right) &= F_{140}\! \left(x , y\right)\\
F_{140}\! \left(x , y\right) &= -\frac{-y F_{141}\! \left(x , y\right)+F_{141}\! \left(x , 1\right)}{-1+y}\\
F_{141}\! \left(x , y\right) &= F_{142}\! \left(x , y\right)\\
F_{142}\! \left(x , y\right) &= F_{101}\! \left(x , y\right) F_{30}\! \left(x \right)\\
F_{143}\! \left(x , y\right) &= -\frac{y \left(F_{54}\! \left(x , 1\right)-F_{54}\! \left(x , y\right)\right)}{-1+y}\\
F_{144}\! \left(x , y\right) &= F_{145}\! \left(x , y\right)\\
F_{145}\! \left(x , y\right) &= F_{146}\! \left(x , y\right) F_{27}\! \left(x , y\right)\\
F_{146}\! \left(x , y\right) &= F_{147}\! \left(x , y\right)+F_{148}\! \left(x , y\right)\\
F_{147}\! \left(x , y\right) &= F_{21}\! \left(x , y\right) F_{74}\! \left(x , y\right)\\
F_{148}\! \left(x , y\right) &= F_{149}\! \left(x , y\right)\\
F_{149}\! \left(x , y\right) &= F_{150}\! \left(x , y\right) F_{24}\! \left(x , y\right)\\
F_{150}\! \left(x , y\right) &= y F_{76}\! \left(x , y\right)\\
F_{151}\! \left(x , y\right) &= F_{152}\! \left(x , y\right)\\
F_{152}\! \left(x , y\right) &= F_{27}\! \left(x , y\right) F_{84}\! \left(x , y\right)\\
F_{153}\! \left(x , y\right) &= F_{154}\! \left(x , y\right)\\
F_{154}\! \left(x , y\right) &= F_{30}\! \left(x \right) F_{81}\! \left(x , y\right)\\
F_{155}\! \left(x \right) &= F_{156}\! \left(x \right)\\
F_{156}\! \left(x \right) &= F_{157}\! \left(x \right) F_{30}\! \left(x \right) F_{97}\! \left(x \right)\\
F_{157}\! \left(x \right) &= F_{158}\! \left(x \right)+F_{161}\! \left(x \right)\\
F_{158}\! \left(x \right) &= F_{159}\! \left(x \right)+F_{160}\! \left(x \right)\\
F_{159}\! \left(x \right) &= F_{23}\! \left(x , 1\right)\\
F_{160}\! \left(x \right) &= F_{9}\! \left(x \right)\\
F_{161}\! \left(x \right) &= F_{9}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Tracked Fusion Tracked Component Fusion Req Corrob Symmetries" and has 171 rules.
Finding the specification took 25133 seconds.
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Copy 171 equations to clipboard:
\(\begin{align*}
F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{1}\! \left(x \right) &= 1\\
F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{30}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{30}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{164}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{11}\! \left(x \right) F_{30}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x , 1\right)\\
F_{12}\! \left(x , y\right) &= F_{13}\! \left(x , y\right)+F_{162}\! \left(x , y\right)\\
F_{14}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{30}\! \left(x \right)\\
F_{14}\! \left(x , y\right) &= F_{15}\! \left(x , y\right)\\
F_{16}\! \left(x , y\right) &= F_{15}\! \left(x , y\right)+F_{23}\! \left(x , y\right)\\
F_{17}\! \left(x , y\right) &= F_{16}\! \left(x , y\right)+F_{160}\! \left(x , y\right)\\
F_{18}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{27}\! \left(x , y\right)\\
F_{18}\! \left(x , y\right) &= F_{19}\! \left(x , y\right)\\
F_{19}\! \left(x , y\right) &= F_{20}\! \left(x , y\right)\\
F_{20}\! \left(x , y\right) &= F_{21}\! \left(x , y\right) F_{27}\! \left(x , y\right)\\
F_{21}\! \left(x , y\right) &= F_{22}\! \left(x , y\right)+F_{33}\! \left(x , y\right)\\
F_{22}\! \left(x , y\right) &= F_{23}\! \left(x , y\right)+F_{31}\! \left(x , y\right)\\
F_{23}\! \left(x , y\right) &= F_{24}\! \left(x , y\right)+F_{28}\! \left(x , y\right)\\
F_{24}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{25}\! \left(x , y\right)\\
F_{25}\! \left(x , y\right) &= F_{26}\! \left(x , y\right)\\
F_{26}\! \left(x , y\right) &= F_{24}\! \left(x , y\right) F_{27}\! \left(x , y\right)\\
F_{27}\! \left(x , y\right) &= y x\\
F_{28}\! \left(x , y\right) &= F_{29}\! \left(x , y\right)\\
F_{29}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{30}\! \left(x \right)\\
F_{30}\! \left(x \right) &= x\\
F_{31}\! \left(x , y\right) &= y F_{32}\! \left(x , y\right)\\
F_{32}\! \left(x , y\right) &= F_{29}\! \left(x , y\right)\\
F_{33}\! \left(x , y\right) &= F_{34}\! \left(x , y\right)\\
F_{34}\! \left(x , y\right) &= F_{30}\! \left(x \right) F_{35}\! \left(x , y\right)\\
F_{36}\! \left(x , y\right) &= F_{27}\! \left(x , y\right) F_{35}\! \left(x , y\right)\\
F_{36}\! \left(x , y\right) &= F_{37}\! \left(x , y\right)\\
F_{37}\! \left(x , y\right) &= F_{19}\! \left(x , y\right)+F_{38}\! \left(x , y\right)\\
F_{38}\! \left(x , y\right) &= F_{39}\! \left(x , y\right)\\
F_{39}\! \left(x , y\right) &= F_{30}\! \left(x \right) F_{40}\! \left(x , y\right)\\
F_{40}\! \left(x , y\right) &= F_{153}\! \left(x , y\right)+F_{41}\! \left(x , y\right)\\
F_{41}\! \left(x , y\right) &= F_{42}\! \left(x , y\right)+F_{43}\! \left(x , y\right)\\
F_{42}\! \left(x , y\right) &= -\frac{y \left(F_{37}\! \left(x , 1\right)-F_{37}\! \left(x , y\right)\right)}{-1+y}\\
F_{44}\! \left(x , y\right) &= F_{139}\! \left(x , y\right)+F_{43}\! \left(x , y\right)\\
F_{44}\! \left(x , y\right) &= F_{45}\! \left(x , y\right)+F_{48}\! \left(x , y\right)\\
F_{45}\! \left(x , y\right) &= F_{2}\! \left(x \right) F_{46}\! \left(x , y\right)\\
F_{46}\! \left(x , y\right) &= F_{47}\! \left(x , y\right)\\
F_{47}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{27}\! \left(x , y\right)\\
F_{48}\! \left(x , y\right) &= F_{49}\! \left(x , y\right)\\
F_{49}\! \left(x , y\right) &= F_{30}\! \left(x \right) F_{50}\! \left(x , y\right)\\
F_{50}\! \left(x , y\right) &= F_{135}\! \left(x , y\right)+F_{51}\! \left(x , y\right)\\
F_{51}\! \left(x , y\right) &= -\frac{y \left(F_{52}\! \left(x , 1\right)-F_{52}\! \left(x , y\right)\right)}{-1+y}\\
F_{52}\! \left(x , y\right) &= F_{133}\! \left(x , y\right)+F_{53}\! \left(x , y\right)\\
F_{53}\! \left(x , y\right) &= F_{0}\! \left(x \right) F_{54}\! \left(x , y\right)\\
F_{55}\! \left(x , y\right) &= F_{54}\! \left(x , y\right)+F_{95}\! \left(x \right)\\
F_{55}\! \left(x , y\right) &= F_{13}\! \left(x , y\right)+F_{56}\! \left(x , y\right)\\
F_{56}\! \left(x , y\right) &= F_{57}\! \left(x , y\right)\\
F_{57}\! \left(x , y\right) &= F_{30}\! \left(x \right) F_{58}\! \left(x , y\right)\\
F_{58}\! \left(x , y\right) &= F_{59}\! \left(x , y\right)+F_{69}\! \left(x , y\right)\\
F_{59}\! \left(x , y\right) &= F_{60}\! \left(x , y\right)+F_{94}\! \left(x , y\right)\\
F_{60}\! \left(x , y\right) &= F_{61}\! \left(x , y\right)+F_{72}\! \left(x , y\right)\\
F_{61}\! \left(x , y\right) &= F_{62}\! \left(x , y\right)+F_{69}\! \left(x , y\right)\\
F_{62}\! \left(x , y\right) &= F_{63}\! \left(x , y\right)+F_{67}\! \left(x , y\right)\\
F_{63}\! \left(x , y\right) &= F_{23}\! \left(x , y\right) F_{64}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{65}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{66}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{30}\! \left(x \right) F_{64}\! \left(x \right)\\
F_{67}\! \left(x , y\right) &= F_{68}\! \left(x , y\right)\\
F_{68}\! \left(x , y\right) &= F_{30}\! \left(x \right) F_{55}\! \left(x , y\right) F_{64}\! \left(x \right)\\
F_{69}\! \left(x , y\right) &= F_{70}\! \left(x , y\right)\\
F_{70}\! \left(x , y\right) &= F_{30}\! \left(x \right) F_{59}\! \left(x , y\right) F_{71}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{64}\! \left(x \right)\\
F_{72}\! \left(x , y\right) &= F_{73}\! \left(x , y\right)\\
F_{73}\! \left(x , y\right) &= F_{30}\! \left(x \right) F_{61}\! \left(x , y\right) F_{74}\! \left(x , y\right)\\
F_{74}\! \left(x , y\right) &= F_{75}\! \left(x , y\right)+F_{76}\! \left(x , y\right)\\
F_{75}\! \left(x , y\right) &= F_{4}\! \left(x \right)+F_{46}\! \left(x , y\right)\\
F_{76}\! \left(x , y\right) &= F_{77}\! \left(x , y\right)\\
F_{77}\! \left(x , y\right) &= F_{30}\! \left(x \right) F_{78}\! \left(x , y\right)\\
F_{78}\! \left(x , y\right) &= F_{13}\! \left(x , y\right)+F_{79}\! \left(x , y\right)\\
F_{79}\! \left(x , y\right) &= F_{80}\! \left(x , y\right)\\
F_{80}\! \left(x , y\right) &= F_{27}\! \left(x , y\right) F_{81}\! \left(x , y\right)\\
F_{81}\! \left(x , y\right) &= F_{82}\! \left(x , y\right)+F_{87}\! \left(x , y\right)\\
F_{82}\! \left(x , y\right) &= F_{83}\! \left(x , y\right)\\
F_{83}\! \left(x , y\right) &= F_{84}\! \left(x , y\right)+F_{92}\! \left(x , y\right)\\
F_{84}\! \left(x , y\right) &= F_{85}\! \left(x , y\right)+F_{89}\! \left(x , y\right)\\
F_{85}\! \left(x , y\right) &= F_{86}\! \left(x , y\right)\\
F_{86}\! \left(x , y\right) &= F_{17}\! \left(x , y\right)+F_{87}\! \left(x , y\right)\\
F_{87}\! \left(x , y\right) &= F_{88}\! \left(x , y\right)\\
F_{88}\! \left(x , y\right) &= F_{30}\! \left(x \right) F_{71}\! \left(x \right) F_{82}\! \left(x , y\right)\\
F_{89}\! \left(x , y\right) &= F_{90}\! \left(x , y\right)\\
F_{90}\! \left(x , y\right) &= F_{30}\! \left(x \right) F_{85}\! \left(x , y\right) F_{91}\! \left(x , y\right)\\
F_{91}\! \left(x , y\right) &= F_{74}\! \left(x , y\right)\\
F_{92}\! \left(x , y\right) &= F_{93}\! \left(x , y\right)\\
F_{93}\! \left(x , y\right) &= F_{24}\! \left(x , y\right) F_{30}\! \left(x \right) F_{78}\! \left(x , y\right)\\
F_{94}\! \left(x , y\right) &= F_{67}\! \left(x , y\right)\\
F_{95}\! \left(x \right) &= F_{96}\! \left(x , 1\right)\\
F_{96}\! \left(x , y\right) &= F_{102}\! \left(x , y\right)+F_{97}\! \left(x \right)\\
F_{97}\! \left(x \right) &= \frac{F_{98}\! \left(x \right)}{F_{30}\! \left(x \right)}\\
F_{98}\! \left(x \right) &= F_{99}\! \left(x \right)\\
F_{99}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{100}\! \left(x \right)\\
F_{100}\! \left(x \right) &= \frac{F_{101}\! \left(x \right)}{F_{30}\! \left(x \right)}\\
F_{101}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{102}\! \left(x , y\right) &= F_{103}\! \left(x , y\right)\\
F_{103}\! \left(x , y\right) &= F_{104}\! \left(x , y\right) F_{27}\! \left(x , y\right)\\
F_{104}\! \left(x , y\right) &= F_{105}\! \left(x , y\right)+F_{132}\! \left(x , y\right)\\
F_{105}\! \left(x , y\right) &= F_{106}\! \left(x , y\right)+F_{131}\! \left(x , y\right)\\
F_{106}\! \left(x , y\right) &= F_{107}\! \left(x , y\right)\\
F_{107}\! \left(x , y\right) &= F_{108}\! \left(x , y\right)+F_{127}\! \left(x , y\right)\\
F_{108}\! \left(x , y\right) &= F_{109}\! \left(x , y\right)\\
F_{109}\! \left(x , y\right) &= F_{110}\! \left(x , y\right)+F_{111}\! \left(x , y\right)\\
F_{110}\! \left(x , y\right) &= F_{100}\! \left(x \right) F_{24}\! \left(x , y\right)\\
F_{111}\! \left(x , y\right) &= F_{112}\! \left(x , y\right)\\
F_{112}\! \left(x , y\right) &= F_{113}\! \left(x , y\right) F_{114}\! \left(x , y\right) F_{30}\! \left(x \right)\\
F_{113}\! \left(x , y\right) &= F_{105}\! \left(x , y\right)\\
F_{114}\! \left(x , y\right) &= F_{115}\! \left(x , y\right)+F_{119}\! \left(x , y\right)\\
F_{115}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{116}\! \left(x , y\right)\\
F_{116}\! \left(x , y\right) &= F_{117}\! \left(x , y\right)\\
F_{117}\! \left(x , y\right) &= F_{115}\! \left(x , y\right) F_{118}\! \left(x , y\right)\\
F_{118}\! \left(x , y\right) &= y x\\
F_{119}\! \left(x , y\right) &= F_{120}\! \left(x \right)+F_{122}\! \left(x , y\right)\\
F_{120}\! \left(x \right) &= F_{121}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{30}\! \left(x \right) F_{71}\! \left(x \right)\\
F_{122}\! \left(x , y\right) &= F_{123}\! \left(x \right)+F_{124}\! \left(x , y\right)+F_{126}\! \left(x , y\right)\\
F_{123}\! \left(x \right) &= 0\\
F_{124}\! \left(x , y\right) &= F_{125}\! \left(x , y\right) F_{30}\! \left(x \right)\\
F_{125}\! \left(x , y\right) &= F_{116}\! \left(x , y\right)+F_{122}\! \left(x , y\right)\\
F_{126}\! \left(x , y\right) &= F_{118}\! \left(x , y\right) F_{119}\! \left(x , y\right)\\
F_{127}\! \left(x , y\right) &= F_{128}\! \left(x , y\right)\\
F_{128}\! \left(x , y\right) &= F_{108}\! \left(x , y\right) F_{129}\! \left(x \right) F_{30}\! \left(x \right)\\
F_{129}\! \left(x \right) &= F_{130}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{130}\! \left(x \right) &= F_{5}\! \left(x \right)\\
F_{131}\! \left(x , y\right) &= F_{24}\! \left(x , y\right) F_{99}\! \left(x \right)\\
F_{132}\! \left(x , y\right) &= F_{111}\! \left(x , y\right)\\
F_{133}\! \left(x , y\right) &= F_{134}\! \left(x , y\right) F_{2}\! \left(x \right)\\
F_{13}\! \left(x , y\right) &= F_{134}\! \left(x , y\right)+F_{97}\! \left(x \right)\\
F_{135}\! \left(x , y\right) &= F_{0}\! \left(x \right) F_{136}\! \left(x , y\right)\\
F_{137}\! \left(x , y\right) &= F_{136}\! \left(x , y\right)+F_{152}\! \left(x , y\right)\\
F_{138}\! \left(x , y\right) &= F_{137}\! \left(x , y\right) F_{30}\! \left(x \right)\\
F_{138}\! \left(x , y\right) &= F_{139}\! \left(x , y\right)\\
F_{139}\! \left(x , y\right) &= F_{140}\! \left(x , y\right)\\
F_{140}\! \left(x , y\right) &= F_{141}\! \left(x , y\right) F_{27}\! \left(x , y\right)\\
F_{141}\! \left(x , y\right) &= F_{142}\! \left(x , y\right)+F_{148}\! \left(x , y\right)\\
F_{142}\! \left(x , y\right) &= -\frac{-F_{143}\! \left(x , y\right)+F_{143}\! \left(x , 1\right)}{-1+y}\\
F_{143}\! \left(x , y\right) &= F_{144}\! \left(x , y\right)\\
F_{144}\! \left(x , y\right) &= F_{145}\! \left(x , y\right) F_{27}\! \left(x , y\right)\\
F_{146}\! \left(x , y\right) &= F_{145}\! \left(x , y\right) F_{27}\! \left(x , y\right)\\
F_{146}\! \left(x , y\right) &= F_{147}\! \left(x , y\right)\\
F_{78}\! \left(x , y\right) &= F_{147}\! \left(x , y\right)+F_{96}\! \left(x , y\right)\\
F_{148}\! \left(x , y\right) &= F_{149}\! \left(x , y\right)\\
F_{149}\! \left(x , y\right) &= -\frac{-y F_{150}\! \left(x , y\right)+F_{150}\! \left(x , 1\right)}{-1+y}\\
F_{150}\! \left(x , y\right) &= F_{151}\! \left(x , y\right)\\
F_{151}\! \left(x , y\right) &= F_{104}\! \left(x , y\right) F_{30}\! \left(x \right)\\
F_{152}\! \left(x , y\right) &= -\frac{y \left(F_{54}\! \left(x , 1\right)-F_{54}\! \left(x , y\right)\right)}{-1+y}\\
F_{153}\! \left(x , y\right) &= F_{154}\! \left(x , y\right)\\
F_{154}\! \left(x , y\right) &= F_{155}\! \left(x , y\right) F_{27}\! \left(x , y\right)\\
F_{155}\! \left(x , y\right) &= F_{156}\! \left(x , y\right)+F_{157}\! \left(x , y\right)\\
F_{156}\! \left(x , y\right) &= F_{21}\! \left(x , y\right) F_{74}\! \left(x , y\right)\\
F_{157}\! \left(x , y\right) &= F_{158}\! \left(x , y\right)\\
F_{158}\! \left(x , y\right) &= F_{159}\! \left(x , y\right) F_{24}\! \left(x , y\right)\\
F_{159}\! \left(x , y\right) &= y F_{76}\! \left(x , y\right)\\
F_{160}\! \left(x , y\right) &= F_{161}\! \left(x , y\right)\\
F_{161}\! \left(x , y\right) &= F_{27}\! \left(x , y\right) F_{86}\! \left(x , y\right)\\
F_{162}\! \left(x , y\right) &= F_{163}\! \left(x , y\right)\\
F_{163}\! \left(x , y\right) &= F_{30}\! \left(x \right) F_{81}\! \left(x , y\right)\\
F_{164}\! \left(x \right) &= F_{165}\! \left(x \right)\\
F_{165}\! \left(x \right) &= F_{100}\! \left(x \right) F_{166}\! \left(x \right) F_{30}\! \left(x \right)\\
F_{166}\! \left(x \right) &= F_{167}\! \left(x \right)+F_{170}\! \left(x \right)\\
F_{167}\! \left(x \right) &= F_{168}\! \left(x \right)+F_{169}\! \left(x \right)\\
F_{168}\! \left(x \right) &= F_{23}\! \left(x , 1\right)\\
F_{169}\! \left(x \right) &= F_{9}\! \left(x \right)\\
F_{170}\! \left(x \right) &= F_{9}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point And Row Placements Tracked Fusion Tracked Component Fusion Req Corrob Symmetries" and has 59 rules.
Finding the specification took 3900 seconds.
Copy 59 equations to clipboard:
\(\begin{align*}
F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{1}\! \left(x \right) &= 1\\
F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{12}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{54}\! \left(x \right)+F_{6}\! \left(x \right)+F_{7}\! \left(x \right)\\
F_{6}\! \left(x \right) &= 0\\
F_{7}\! \left(x \right) &= F_{12}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{9}\! \left(x , 1\right)\\
F_{9}\! \left(x , y\right) &= F_{10}\! \left(x , y\right)+F_{28}\! \left(x , y\right)\\
F_{10}\! \left(x , y\right) &= F_{11}\! \left(x , y\right)+F_{13}\! \left(x , y\right)+F_{6}\! \left(x \right)\\
F_{11}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{9}\! \left(x , y\right)\\
F_{12}\! \left(x \right) &= x\\
F_{13}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{21}\! \left(x , y\right)\\
F_{14}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{13}\! \left(x , y\right)+F_{15}\! \left(x , y\right)+F_{20}\! \left(x , y\right)\\
F_{15}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{16}\! \left(x , y\right)\\
F_{16}\! \left(x , y\right) &= F_{17}\! \left(x , y\right)+F_{26}\! \left(x , y\right)\\
F_{17}\! \left(x , y\right) &= F_{18}\! \left(x , y\right)+F_{22}\! \left(x , y\right)\\
F_{18}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{19}\! \left(x , y\right)+F_{20}\! \left(x , y\right)\\
F_{19}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{17}\! \left(x , y\right)\\
F_{20}\! \left(x , y\right) &= F_{18}\! \left(x , y\right) F_{21}\! \left(x , y\right)\\
F_{21}\! \left(x , y\right) &= y x\\
F_{22}\! \left(x , y\right) &= F_{23}\! \left(x , y\right)\\
F_{23}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{24}\! \left(x , y\right)\\
F_{25}\! \left(x , y\right) &= F_{21}\! \left(x , y\right) F_{24}\! \left(x , y\right)\\
F_{25}\! \left(x , y\right) &= F_{9}\! \left(x , y\right)\\
F_{26}\! \left(x , y\right) &= y F_{27}\! \left(x , y\right)\\
F_{27}\! \left(x , y\right) &= F_{23}\! \left(x , y\right)\\
F_{28}\! \left(x , y\right) &= F_{29}\! \left(x , y\right)\\
F_{29}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{30}\! \left(x , y\right)\\
F_{30}\! \left(x , y\right) &= F_{31}\! \left(x , y\right)+F_{42}\! \left(x , y\right)\\
F_{31}\! \left(x , y\right) &= F_{32}\! \left(x , y\right)+F_{33}\! \left(x , y\right)\\
F_{32}\! \left(x , y\right) &= -\frac{y \left(F_{9}\! \left(x , 1\right)-F_{9}\! \left(x , y\right)\right)}{-1+y}\\
F_{33}\! \left(x , y\right) &= F_{34}\! \left(x , y\right)\\
F_{34}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{35}\! \left(x , y\right) F_{40}\! \left(x \right)\\
F_{35}\! \left(x , y\right) &= -\frac{y \left(F_{36}\! \left(x , 1\right)-F_{36}\! \left(x , y\right)\right)}{-1+y}\\
F_{37}\! \left(x , y\right) &= F_{36}\! \left(x , y\right)+F_{38}\! \left(x \right)\\
F_{37}\! \left(x , y\right) &= F_{17}\! \left(x , y\right)+F_{27}\! \left(x , y\right)\\
F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{5}\! \left(x \right)\\
F_{40}\! \left(x \right) &= \frac{F_{41}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{41}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{42}\! \left(x , y\right) &= F_{43}\! \left(x , y\right)+F_{45}\! \left(x , y\right)+F_{6}\! \left(x \right)\\
F_{43}\! \left(x , y\right) &= F_{44}\! \left(x , y\right)\\
F_{44}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{37}\! \left(x , y\right) F_{9}\! \left(x , y\right)\\
F_{45}\! \left(x , y\right) &= F_{46}\! \left(x , y\right)\\
F_{46}\! \left(x , y\right) &= F_{21}\! \left(x , y\right) F_{47}\! \left(x , y\right)\\
F_{47}\! \left(x , y\right) &= F_{48}\! \left(x , y\right)+F_{49}\! \left(x , y\right)\\
F_{48}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{37}\! \left(x , y\right)\\
F_{49}\! \left(x , y\right) &= F_{50}\! \left(x , y\right)\\
F_{50}\! \left(x , y\right) &= F_{26}\! \left(x , y\right) F_{51}\! \left(x , y\right)\\
F_{51}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{52}\! \left(x , y\right)\\
F_{52}\! \left(x , y\right) &= F_{53}\! \left(x , y\right)\\
F_{53}\! \left(x , y\right) &= F_{21}\! \left(x , y\right) F_{51}\! \left(x , y\right)\\
F_{54}\! \left(x \right) &= F_{12}\! \left(x \right) F_{55}\! \left(x \right)\\
F_{55}\! \left(x \right) &= F_{4}\! \left(x \right)+F_{56}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{57}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{12}\! \left(x \right) F_{4}\! \left(x \right) F_{58}\! \left(x \right)\\
F_{58}\! \left(x \right) &= F_{37}\! \left(x , 1\right)\\
\end{align*}\)