Av(12453, 12543, 13452, 13542, 14352, 23451, 23541, 24351, 34251)
Counting Sequence
1, 1, 2, 6, 24, 111, 548, 2800, 14625, 77628, 417311, 2267122, 12427759, 68659812, 381940180, ...
Implicit Equation for the Generating Function
\(\displaystyle 3 x^{3} \left(2 x^{3}-6 x^{2}+4 x -1\right) \left(x -1\right)^{4} \left(x^{3}-3 x^{2}+4 x -1\right)^{4} F \left(x
\right)^{4}+x^{2} \left(3 x^{9}-39 x^{8}+213 x^{7}-626 x^{6}+1078 x^{5}-1159 x^{4}+751 x^{3}-287 x^{2}+59 x -5\right) \left(x -1\right)^{3} \left(x^{3}-3 x^{2}+4 x -1\right)^{3} F \left(x
\right)^{3}+x \left(18 x^{13}-268 x^{12}+1743 x^{11}-6584 x^{10}+16170 x^{9}-27404 x^{8}+32954 x^{7}-28433 x^{6}+17495 x^{5}-7546 x^{4}+2208 x^{3}-413 x^{2}+44 x -2\right) \left(x -1\right)^{2} \left(x^{3}-3 x^{2}+4 x -1\right)^{2} F \left(x
\right)^{2}+\left(x -1\right) \left(x^{3}-3 x^{2}+4 x -1\right) \left(24 x^{17}-392 x^{16}+2881 x^{15}-12630 x^{14}+36987 x^{13}-76701 x^{12}+115933 x^{11}-128668 x^{10}+102928 x^{9}-55254 x^{8}+14573 x^{7}+4281 x^{6}-6478 x^{5}+3357 x^{4}-1027 x^{3}+194 x^{2}-21 x +1\right) F \! \left(x \right)-1+132 x^{19}-1128 x^{18}-8 x^{20}+27 x -337 x^{2}+52969 x^{5}-13668 x^{4}+2585 x^{3}+498875 x^{13}-811815 x^{12}+1061317 x^{11}-1119325 x^{10}+953190 x^{9}-653811 x^{8}+359022 x^{7}-156187 x^{6}+6581 x^{17}-28510 x^{16}+94589 x^{15}-244500 x^{14} = 0\)
Recurrence
\(\displaystyle a(0) = 1\)
\(\displaystyle a(1) = 1\)
\(\displaystyle a(2) = 2\)
\(\displaystyle a(3) = 6\)
\(\displaystyle a(4) = 24\)
\(\displaystyle a(5) = 111\)
\(\displaystyle a(6) = 548\)
\(\displaystyle a(7) = 2800\)
\(\displaystyle a(8) = 14625\)
\(\displaystyle a(9) = 77628\)
\(\displaystyle a(10) = 417311\)
\(\displaystyle a(11) = 2267122\)
\(\displaystyle a(12) = 12427759\)
\(\displaystyle a(13) = 68659812\)
\(\displaystyle a(14) = 381940180\)
\(\displaystyle a(15) = 2137633473\)
\(\displaystyle a(16) = 12029055784\)
\(\displaystyle a(17) = 68021637410\)
\(\displaystyle a(18) = 386340662510\)
\(\displaystyle a(19) = 2203027921631\)
\(\displaystyle a(20) = 12607752234432\)
\(\displaystyle a(21) = 72391074887448\)
\(\displaystyle a(22) = 416908260663967\)
\(\displaystyle a(23) = 2407669414423227\)
\(\displaystyle a(24) = 13939883504415302\)
\(\displaystyle a(25) = 80898967996788517\)
\(\displaystyle a(26) = 470514587978588629\)
\(\displaystyle a(27) = 2742092435846669588\)
\(\displaystyle a(28) = 16010667465106928150\)
\(\displaystyle a(29) = 93648444666818797733\)
\(\displaystyle a(30) = 548663598305335710461\)
\(\displaystyle a(31) = 3219448078668574248199\)
\(\displaystyle a(32) = 18918456499538102309874\)
\(\displaystyle a(33) = 111322217346564988115472\)
\(\displaystyle a(34) = 655897410862116993384893\)
\(\displaystyle a(35) = 3869160805951475557599174\)
\(\displaystyle a(36) = 22850506660444958343859520\)
\(\displaystyle a(37) = 135097320116732303072268272\)
\(\displaystyle a(38) = 799549144778639403713900275\)
\(\displaystyle a{\left(n + 37 \right)} = - \frac{34957008 \left(n - 1\right) \left(n + 1\right) \left(n + 2\right) a{\left(n \right)}}{2387 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} + \frac{104976 \left(n + 2\right) \left(11387 n^{2} + 29231 n + 1998\right) a{\left(n + 1 \right)}}{2387 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} + \frac{9 \left(12161 n + 429105\right) a{\left(n + 36 \right)}}{2387 \left(n + 38\right)} - \frac{\left(2347875 n^{2} + 163354001 n + 2841291284\right) a{\left(n + 35 \right)}}{2387 \left(n + 37\right) \left(n + 38\right)} - \frac{128 \left(3116 n^{3} + 81972 n^{2} - 2165723 n - 307908\right)}{7161 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} - \frac{34992 \left(516089 n^{3} + 3770162 n^{2} + 8518446 n + 5549601\right) a{\left(n + 2 \right)}}{2387 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} + \frac{2916 \left(55700251 n^{3} + 562174966 n^{2} + 1833191489 n + 1901830682\right) a{\left(n + 3 \right)}}{2387 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} + \frac{\left(93497594 n^{3} + 9620922555 n^{2} + 329970621307 n + 3772050764334\right) a{\left(n + 34 \right)}}{7161 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} - \frac{\left(567386475 n^{3} + 56918404631 n^{2} + 1903247794780 n + 21213301199936\right) a{\left(n + 33 \right)}}{4774 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} - \frac{324 \left(3010006726 n^{3} + 38807582133 n^{2} + 164121306419 n + 226611273678\right) a{\left(n + 4 \right)}}{2387 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} + \frac{\left(10995278231 n^{3} + 1077086647968 n^{2} + 35171245359373 n + 382840640670456\right) a{\left(n + 32 \right)}}{14322 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} + \frac{108 \left(38560177069 n^{3} + 607097008351 n^{2} + 3154707889922 n + 5401640385026\right) a{\left(n + 5 \right)}}{2387 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} - \frac{\left(48778331965 n^{3} + 4695680678061 n^{2} + 150664763335430 n + 1611257880569220\right) a{\left(n + 31 \right)}}{14322 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} + \frac{\left(80667931601 n^{3} + 5503845711358 n^{2} + 113164977624109 n + 619688311128996\right) a{\left(n + 29 \right)}}{4774 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} + \frac{\left(115302980236 n^{3} + 11318813374455 n^{2} + 369054204719789 n + 3998230091751774\right) a{\left(n + 30 \right)}}{14322 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} - \frac{108 \left(122292913447 n^{3} + 2294026116416 n^{2} + 14237531609299 n + 29215003092332\right) a{\left(n + 6 \right)}}{2387 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} - \frac{\left(4173665399665 n^{3} + 332553783728607 n^{2} + 8768629499805500 n + 76407287620381428\right) a{\left(n + 28 \right)}}{14322 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} + \frac{6 \left(5370713882915 n^{3} + 118890683909004 n^{2} + 870726751582579 n + 2109161775885594\right) a{\left(n + 7 \right)}}{2387 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} + \frac{\left(8374798549385 n^{3} + 658822845453038 n^{2} + 17208240559779471 n + 149163007207008442\right) a{\left(n + 27 \right)}}{4774 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} - \frac{4 \left(13020871031519 n^{3} + 996587705068962 n^{2} + 25347385206989953 n + 214166593555279635\right) a{\left(n + 26 \right)}}{7161 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} + \frac{2 \left(27705648762916 n^{3} + 2053207520815501 n^{2} + 50576286578152967 n + 413994703684004700\right) a{\left(n + 25 \right)}}{2387 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} - \frac{\left(62412116743747 n^{3} + 1634327364920272 n^{2} + 14102555137853207 n + 40125489227639486\right) a{\left(n + 8 \right)}}{2387 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} + \frac{3 \left(85572447190268 n^{3} + 1072325940841755 n^{2} - 10541516703972617 n - 132057781095629978\right) a{\left(n + 12 \right)}}{4774 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} + \frac{\left(97748277906882 n^{3} + 3063442739930263 n^{2} + 31243409903138809 n + 104142575631351610\right) a{\left(n + 9 \right)}}{2387 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} - \frac{\left(118350664340012 n^{3} + 4578894206059637 n^{2} + 55763108694211747 n + 217664729111628372\right) a{\left(n + 10 \right)}}{2387 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} + \frac{\left(148423176555615 n^{3} + 8807653132214808 n^{2} + 138694789266970231 n + 655716581591271166\right) a{\left(n + 11 \right)}}{4774 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} - \frac{\left(732615500147447 n^{3} + 29100640686791427 n^{2} + 331975416930409678 n + 842811640820924874\right) a{\left(n + 19 \right)}}{7161 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} - \frac{\left(845364969148891 n^{3} + 60528876793643661 n^{2} + 1440481231381966586 n + 11391290052698974368\right) a{\left(n + 24 \right)}}{14322 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} - \frac{\left(1169797403897313 n^{3} + 37697678825106895 n^{2} + 390286112464586266 n + 1277175156886212790\right) a{\left(n + 13 \right)}}{4774 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} + \frac{\left(1269839463530441 n^{3} + 48583575499191950 n^{2} + 616023313044385147 n + 2589278892367236869\right) a{\left(n + 14 \right)}}{2387 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} - \frac{\left(1627711451767253 n^{3} + 77674242064930665 n^{2} + 1234520791285477324 n + 6540626524670338884\right) a{\left(n + 17 \right)}}{2046 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} + \frac{\left(1721110385888404 n^{3} + 118998764270495055 n^{2} + 2733696236519129099 n + 20860778615271137112\right) a{\left(n + 23 \right)}}{14322 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} - \frac{\left(2042764438277065 n^{3} + 138136221656554302 n^{2} + 3040037075056465499 n + 21863915469231129642\right) a{\left(n + 20 \right)}}{14322 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} - \frac{\left(2750466633531670 n^{3} + 183978653163005673 n^{2} + 4085150415649735925 n + 30105176390898770448\right) a{\left(n + 22 \right)}}{14322 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} + \frac{\left(3217361088283666 n^{3} + 210137290531019031 n^{2} + 4543751500396483865 n + 32527799673785026950\right) a{\left(n + 21 \right)}}{14322 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} + \frac{\left(3327843522393404 n^{3} + 162939218876877459 n^{2} + 2650548875724320905 n + 14342685387523033380\right) a{\left(n + 18 \right)}}{7161 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} - \frac{\left(3876306166685537 n^{3} + 163487703268474800 n^{2} + 2294682070757138741 n + 10725510832737771744\right) a{\left(n + 15 \right)}}{4774 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} + \frac{\left(13321909964807854 n^{3} + 602975376912096387 n^{2} + 9090550913270268377 n + 45681734586016781628\right) a{\left(n + 16 \right)}}{14322 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)}, \quad n \geq 39\)
\(\displaystyle a(1) = 1\)
\(\displaystyle a(2) = 2\)
\(\displaystyle a(3) = 6\)
\(\displaystyle a(4) = 24\)
\(\displaystyle a(5) = 111\)
\(\displaystyle a(6) = 548\)
\(\displaystyle a(7) = 2800\)
\(\displaystyle a(8) = 14625\)
\(\displaystyle a(9) = 77628\)
\(\displaystyle a(10) = 417311\)
\(\displaystyle a(11) = 2267122\)
\(\displaystyle a(12) = 12427759\)
\(\displaystyle a(13) = 68659812\)
\(\displaystyle a(14) = 381940180\)
\(\displaystyle a(15) = 2137633473\)
\(\displaystyle a(16) = 12029055784\)
\(\displaystyle a(17) = 68021637410\)
\(\displaystyle a(18) = 386340662510\)
\(\displaystyle a(19) = 2203027921631\)
\(\displaystyle a(20) = 12607752234432\)
\(\displaystyle a(21) = 72391074887448\)
\(\displaystyle a(22) = 416908260663967\)
\(\displaystyle a(23) = 2407669414423227\)
\(\displaystyle a(24) = 13939883504415302\)
\(\displaystyle a(25) = 80898967996788517\)
\(\displaystyle a(26) = 470514587978588629\)
\(\displaystyle a(27) = 2742092435846669588\)
\(\displaystyle a(28) = 16010667465106928150\)
\(\displaystyle a(29) = 93648444666818797733\)
\(\displaystyle a(30) = 548663598305335710461\)
\(\displaystyle a(31) = 3219448078668574248199\)
\(\displaystyle a(32) = 18918456499538102309874\)
\(\displaystyle a(33) = 111322217346564988115472\)
\(\displaystyle a(34) = 655897410862116993384893\)
\(\displaystyle a(35) = 3869160805951475557599174\)
\(\displaystyle a(36) = 22850506660444958343859520\)
\(\displaystyle a(37) = 135097320116732303072268272\)
\(\displaystyle a(38) = 799549144778639403713900275\)
\(\displaystyle a{\left(n + 37 \right)} = - \frac{34957008 \left(n - 1\right) \left(n + 1\right) \left(n + 2\right) a{\left(n \right)}}{2387 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} + \frac{104976 \left(n + 2\right) \left(11387 n^{2} + 29231 n + 1998\right) a{\left(n + 1 \right)}}{2387 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} + \frac{9 \left(12161 n + 429105\right) a{\left(n + 36 \right)}}{2387 \left(n + 38\right)} - \frac{\left(2347875 n^{2} + 163354001 n + 2841291284\right) a{\left(n + 35 \right)}}{2387 \left(n + 37\right) \left(n + 38\right)} - \frac{128 \left(3116 n^{3} + 81972 n^{2} - 2165723 n - 307908\right)}{7161 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} - \frac{34992 \left(516089 n^{3} + 3770162 n^{2} + 8518446 n + 5549601\right) a{\left(n + 2 \right)}}{2387 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} + \frac{2916 \left(55700251 n^{3} + 562174966 n^{2} + 1833191489 n + 1901830682\right) a{\left(n + 3 \right)}}{2387 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} + \frac{\left(93497594 n^{3} + 9620922555 n^{2} + 329970621307 n + 3772050764334\right) a{\left(n + 34 \right)}}{7161 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} - \frac{\left(567386475 n^{3} + 56918404631 n^{2} + 1903247794780 n + 21213301199936\right) a{\left(n + 33 \right)}}{4774 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} - \frac{324 \left(3010006726 n^{3} + 38807582133 n^{2} + 164121306419 n + 226611273678\right) a{\left(n + 4 \right)}}{2387 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} + \frac{\left(10995278231 n^{3} + 1077086647968 n^{2} + 35171245359373 n + 382840640670456\right) a{\left(n + 32 \right)}}{14322 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} + \frac{108 \left(38560177069 n^{3} + 607097008351 n^{2} + 3154707889922 n + 5401640385026\right) a{\left(n + 5 \right)}}{2387 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} - \frac{\left(48778331965 n^{3} + 4695680678061 n^{2} + 150664763335430 n + 1611257880569220\right) a{\left(n + 31 \right)}}{14322 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} + \frac{\left(80667931601 n^{3} + 5503845711358 n^{2} + 113164977624109 n + 619688311128996\right) a{\left(n + 29 \right)}}{4774 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} + \frac{\left(115302980236 n^{3} + 11318813374455 n^{2} + 369054204719789 n + 3998230091751774\right) a{\left(n + 30 \right)}}{14322 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} - \frac{108 \left(122292913447 n^{3} + 2294026116416 n^{2} + 14237531609299 n + 29215003092332\right) a{\left(n + 6 \right)}}{2387 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} - \frac{\left(4173665399665 n^{3} + 332553783728607 n^{2} + 8768629499805500 n + 76407287620381428\right) a{\left(n + 28 \right)}}{14322 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} + \frac{6 \left(5370713882915 n^{3} + 118890683909004 n^{2} + 870726751582579 n + 2109161775885594\right) a{\left(n + 7 \right)}}{2387 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} + \frac{\left(8374798549385 n^{3} + 658822845453038 n^{2} + 17208240559779471 n + 149163007207008442\right) a{\left(n + 27 \right)}}{4774 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} - \frac{4 \left(13020871031519 n^{3} + 996587705068962 n^{2} + 25347385206989953 n + 214166593555279635\right) a{\left(n + 26 \right)}}{7161 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} + \frac{2 \left(27705648762916 n^{3} + 2053207520815501 n^{2} + 50576286578152967 n + 413994703684004700\right) a{\left(n + 25 \right)}}{2387 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} - \frac{\left(62412116743747 n^{3} + 1634327364920272 n^{2} + 14102555137853207 n + 40125489227639486\right) a{\left(n + 8 \right)}}{2387 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} + \frac{3 \left(85572447190268 n^{3} + 1072325940841755 n^{2} - 10541516703972617 n - 132057781095629978\right) a{\left(n + 12 \right)}}{4774 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} + \frac{\left(97748277906882 n^{3} + 3063442739930263 n^{2} + 31243409903138809 n + 104142575631351610\right) a{\left(n + 9 \right)}}{2387 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} - \frac{\left(118350664340012 n^{3} + 4578894206059637 n^{2} + 55763108694211747 n + 217664729111628372\right) a{\left(n + 10 \right)}}{2387 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} + \frac{\left(148423176555615 n^{3} + 8807653132214808 n^{2} + 138694789266970231 n + 655716581591271166\right) a{\left(n + 11 \right)}}{4774 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} - \frac{\left(732615500147447 n^{3} + 29100640686791427 n^{2} + 331975416930409678 n + 842811640820924874\right) a{\left(n + 19 \right)}}{7161 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} - \frac{\left(845364969148891 n^{3} + 60528876793643661 n^{2} + 1440481231381966586 n + 11391290052698974368\right) a{\left(n + 24 \right)}}{14322 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} - \frac{\left(1169797403897313 n^{3} + 37697678825106895 n^{2} + 390286112464586266 n + 1277175156886212790\right) a{\left(n + 13 \right)}}{4774 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} + \frac{\left(1269839463530441 n^{3} + 48583575499191950 n^{2} + 616023313044385147 n + 2589278892367236869\right) a{\left(n + 14 \right)}}{2387 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} - \frac{\left(1627711451767253 n^{3} + 77674242064930665 n^{2} + 1234520791285477324 n + 6540626524670338884\right) a{\left(n + 17 \right)}}{2046 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} + \frac{\left(1721110385888404 n^{3} + 118998764270495055 n^{2} + 2733696236519129099 n + 20860778615271137112\right) a{\left(n + 23 \right)}}{14322 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} - \frac{\left(2042764438277065 n^{3} + 138136221656554302 n^{2} + 3040037075056465499 n + 21863915469231129642\right) a{\left(n + 20 \right)}}{14322 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} - \frac{\left(2750466633531670 n^{3} + 183978653163005673 n^{2} + 4085150415649735925 n + 30105176390898770448\right) a{\left(n + 22 \right)}}{14322 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} + \frac{\left(3217361088283666 n^{3} + 210137290531019031 n^{2} + 4543751500396483865 n + 32527799673785026950\right) a{\left(n + 21 \right)}}{14322 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} + \frac{\left(3327843522393404 n^{3} + 162939218876877459 n^{2} + 2650548875724320905 n + 14342685387523033380\right) a{\left(n + 18 \right)}}{7161 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} - \frac{\left(3876306166685537 n^{3} + 163487703268474800 n^{2} + 2294682070757138741 n + 10725510832737771744\right) a{\left(n + 15 \right)}}{4774 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)} + \frac{\left(13321909964807854 n^{3} + 602975376912096387 n^{2} + 9090550913270268377 n + 45681734586016781628\right) a{\left(n + 16 \right)}}{14322 \left(n + 36\right) \left(n + 37\right) \left(n + 38\right)}, \quad n \geq 39\)
This specification was found using the strategy pack "Point Placements Tracked Fusion Tracked Component Fusion Symmetries" and has 230 rules.
Finding the specification took 9282 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_{4}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{4}\! \left(x \right) &= x\\
F_{5}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{7}\! \left(x , 1\right)\\
F_{7}\! \left(x , y\right) &= F_{8}\! \left(x , y\right)\\
F_{8}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{9}\! \left(x , y\right)\\
F_{9}\! \left(x , y\right) &= F_{10}\! \left(x , y\right)+F_{116}\! \left(x , y\right)\\
F_{10}\! \left(x , y\right) &= F_{11}\! \left(x , y\right)+F_{93}\! \left(x , y\right)\\
F_{11}\! \left(x , y\right) &= F_{12}\! \left(x , y\right)+F_{23}\! \left(x , y\right)\\
F_{12}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{13}\! \left(x , y\right)\\
F_{13}\! \left(x , y\right) &= F_{14}\! \left(x , y\right)\\
F_{14}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{17}\! \left(x , y\right)\\
F_{15}\! \left(x , y\right) &= F_{12}\! \left(x , y\right)+F_{16}\! \left(x , y\right)\\
F_{16}\! \left(x , y\right) &= F_{17}\! \left(x , y\right)+F_{18}\! \left(x , y\right)\\
F_{17}\! \left(x , y\right) &= y x\\
F_{18}\! \left(x , y\right) &= F_{19}\! \left(x \right)+F_{20}\! \left(x , y\right)+F_{21}\! \left(x , y\right)\\
F_{19}\! \left(x \right) &= 0\\
F_{20}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{17}\! \left(x , y\right)\\
F_{21}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{22}\! \left(x , y\right)\\
F_{22}\! \left(x , y\right) &= F_{16}\! \left(x , y\right)\\
F_{23}\! \left(x , y\right) &= F_{2}\! \left(x \right)+F_{24}\! \left(x , y\right)\\
F_{24}\! \left(x , y\right) &= F_{25}\! \left(x , y\right)\\
F_{25}\! \left(x , y\right) &= F_{12}\! \left(x , y\right) F_{17}\! \left(x , y\right) F_{26}\! \left(x \right) F_{88}\! \left(x , y\right)\\
F_{26}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{27}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)+F_{33}\! \left(x \right)\\
F_{28}\! \left(x \right) &= F_{2}\! \left(x \right) F_{29}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{30}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{31}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{32}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{30}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{31}\! \left(x \right) F_{34}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{36}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{37}\! \left(x \right)+F_{55}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{38}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{39}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{37}\! \left(x \right)+F_{40}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{4}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{42}\! \left(x \right)+F_{53}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{4}\! \left(x \right) F_{43}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{44}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{4}\! \left(x \right) F_{45}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{46}\! \left(x \right)+F_{47}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{43}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{48}\! \left(x \right)+F_{50}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{29}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{51}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{4}\! \left(x \right) F_{52}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{43}\! \left(x \right)+F_{50}\! \left(x \right)\\
F_{53}\! \left(x \right) &= F_{4}\! \left(x \right) F_{54}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{40}\! \left(x \right)\\
F_{55}\! \left(x \right) &= F_{56}\! \left(x \right)+F_{63}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{57}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{4}\! \left(x \right) F_{58}\! \left(x \right)\\
F_{58}\! \left(x \right) &= F_{59}\! \left(x \right)+F_{60}\! \left(x \right)\\
F_{59}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{60}\! \left(x \right) &= F_{56}\! \left(x \right)+F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{62}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{4}\! \left(x \right) F_{56}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{64}\! \left(x \right)+F_{73}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{4}\! \left(x \right) F_{65}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{66}\! \left(x \right)+F_{67}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{41}\! \left(x \right)+F_{43}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{63}\! \left(x \right)+F_{68}\! \left(x \right)\\
F_{68}\! \left(x \right) &= 2 F_{19}\! \left(x \right)+F_{69}\! \left(x \right)+F_{70}\! \left(x \right)\\
F_{69}\! \left(x \right) &= F_{4}\! \left(x \right) F_{63}\! \left(x \right)\\
F_{70}\! \left(x \right) &= F_{4}\! \left(x \right) F_{71}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{72}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{61}\! \left(x \right)+F_{68}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{4}\! \left(x \right) F_{74}\! \left(x \right)\\
F_{74}\! \left(x \right) &= F_{55}\! \left(x \right)+F_{75}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{76}\! \left(x \right)+F_{81}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{62}\! \left(x \right)+F_{77}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{4}\! \left(x \right) F_{78}\! \left(x \right)\\
F_{78}\! \left(x \right) &= F_{79}\! \left(x \right)+F_{80}\! \left(x \right)\\
F_{79}\! \left(x \right) &= F_{4}\! \left(x \right)\\
F_{80}\! \left(x \right) &= F_{61}\! \left(x \right)\\
F_{81}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{69}\! \left(x \right)+F_{82}\! \left(x \right)+F_{86}\! \left(x \right)\\
F_{82}\! \left(x \right) &= F_{4}\! \left(x \right) F_{83}\! \left(x \right)\\
F_{83}\! \left(x \right) &= F_{84}\! \left(x \right)+F_{85}\! \left(x \right)\\
F_{84}\! \left(x \right) &= F_{41}\! \left(x \right)\\
F_{85}\! \left(x \right) &= F_{68}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{4}\! \left(x \right) F_{87}\! \left(x \right)\\
F_{87}\! \left(x \right) &= F_{75}\! \left(x \right)\\
F_{88}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{89}\! \left(x , y\right)\\
F_{89}\! \left(x , y\right) &= F_{90}\! \left(x , y\right)\\
F_{90}\! \left(x , y\right) &= F_{91}\! \left(x , y\right)\\
F_{91}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{92}\! \left(x , y\right)\\
F_{92}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{90}\! \left(x , y\right)\\
F_{93}\! \left(x , y\right) &= F_{94}\! \left(x \right)+F_{97}\! \left(x , y\right)\\
F_{94}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{95}\! \left(x \right)\\
F_{95}\! \left(x \right) &= \frac{F_{96}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{96}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{97}\! \left(x , y\right) &= F_{98}\! \left(x , y\right)\\
F_{98}\! \left(x , y\right) &= F_{99}\! \left(x , y\right)\\
F_{99}\! \left(x , y\right) &= F_{100}\! \left(x , y\right) F_{4}\! \left(x \right)\\
F_{100}\! \left(x , y\right) &= F_{101}\! \left(x , y\right)\\
F_{101}\! \left(x , y\right) &= F_{102}\! \left(x \right) F_{12}\! \left(x , y\right) F_{17}\! \left(x , y\right) F_{88}\! \left(x , y\right)\\
F_{102}\! \left(x \right) &= \frac{F_{103}\! \left(x \right)}{F_{29}\! \left(x \right) F_{4}\! \left(x \right)}\\
F_{103}\! \left(x \right) &= F_{104}\! \left(x \right)\\
F_{104}\! \left(x \right) &= -F_{107}\! \left(x \right)+F_{105}\! \left(x \right)\\
F_{105}\! \left(x \right) &= \frac{F_{106}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{106}\! \left(x \right) &= F_{94}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{108}\! \left(x , 1\right)\\
F_{108}\! \left(x , y\right) &= F_{109}\! \left(x , y\right)+F_{110}\! \left(x , y\right)\\
F_{109}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{7}\! \left(x , y\right)\\
F_{110}\! \left(x , y\right) &= F_{111}\! \left(x , y\right)\\
F_{111}\! \left(x , y\right) &= F_{112}\! \left(x , y\right) F_{4}\! \left(x \right)\\
F_{112}\! \left(x , y\right) &= -\frac{-F_{113}\! \left(x , y\right) y +F_{113}\! \left(x , 1\right)}{-1+y}\\
F_{113}\! \left(x , y\right) &= F_{108}\! \left(x , y\right)+F_{114}\! \left(x , y\right)\\
F_{114}\! \left(x , y\right) &= F_{115}\! \left(x , y\right)\\
F_{115}\! \left(x , y\right) &= F_{102}\! \left(x \right) F_{4}\! \left(x \right) F_{88}\! \left(x , y\right)\\
F_{116}\! \left(x , y\right) &= F_{117}\! \left(x , y\right)+F_{118}\! \left(x , y\right)\\
F_{108}\! \left(x , y\right) &= F_{117}\! \left(x , y\right)+F_{95}\! \left(x \right)\\
F_{118}\! \left(x , y\right) &= F_{119}\! \left(x , y\right)\\
F_{119}\! \left(x , y\right) &= F_{12}\! \left(x , y\right) F_{120}\! \left(x , y\right) F_{17}\! \left(x , y\right) F_{88}\! \left(x , y\right)\\
F_{121}\! \left(x , y\right) &= F_{120}\! \left(x , y\right) F_{29}\! \left(x \right) F_{4}\! \left(x \right) F_{46}\! \left(x \right)\\
F_{121}\! \left(x , y\right) &= F_{122}\! \left(x , y\right)\\
F_{122}\! \left(x , y\right) &= F_{123}\! \left(x , y\right) F_{17}\! \left(x , y\right)\\
F_{123}\! \left(x , y\right) &= F_{124}\! \left(x , y\right)+F_{132}\! \left(x , y\right)\\
F_{124}\! \left(x , y\right) &= F_{125}\! \left(x , y\right) F_{43}\! \left(x \right)\\
F_{126}\! \left(x , y\right) &= F_{125}\! \left(x , y\right)+F_{131}\! \left(x , y\right)\\
F_{127}\! \left(x , y\right) &= F_{126}\! \left(x , y\right) F_{17}\! \left(x , y\right)\\
F_{127}\! \left(x , y\right) &= F_{128}\! \left(x , y\right)\\
F_{128}\! \left(x , y\right) &= F_{117}\! \left(x , y\right)+F_{129}\! \left(x , y\right)\\
F_{129}\! \left(x , y\right) &= F_{130}\! \left(x , y\right)\\
F_{130}\! \left(x , y\right) &= F_{102}\! \left(x \right) F_{4}\! \left(x \right) F_{89}\! \left(x , y\right)\\
F_{131}\! \left(x , y\right) &= F_{114}\! \left(x , y\right)\\
F_{133}\! \left(x , y\right) &= F_{132}\! \left(x , y\right)+F_{229}\! \left(x , y\right)\\
F_{134}\! \left(x , y\right) &= F_{133}\! \left(x , y\right) F_{17}\! \left(x , y\right)\\
F_{134}\! \left(x , y\right) &= F_{135}\! \left(x , y\right)\\
F_{136}\! \left(x , y\right) &= F_{135}\! \left(x , y\right)+F_{228}\! \left(x \right)\\
F_{136}\! \left(x , y\right) &= F_{137}\! \left(x , y\right)+F_{215}\! \left(x , y\right)\\
F_{137}\! \left(x , y\right) &= F_{138}\! \left(x , y\right)+F_{199}\! \left(x , y\right)\\
F_{139}\! \left(x , y\right) &= F_{138}\! \left(x , y\right)+F_{191}\! \left(x , y\right)\\
F_{139}\! \left(x , y\right) &= F_{140}\! \left(x , y\right)+F_{182}\! \left(x , y\right)\\
F_{140}\! \left(x , y\right) &= F_{141}\! \left(x , y\right)+F_{142}\! \left(x , y\right)\\
F_{141}\! \left(x , y\right) &= F_{0}\! \left(x \right) F_{88}\! \left(x , y\right)\\
F_{142}\! \left(x , y\right) &= F_{143}\! \left(x , y\right) F_{30}\! \left(x \right)\\
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_{17}\! \left(x , y\right)\\
F_{145}\! \left(x , y\right) &= F_{146}\! \left(x , y\right)+F_{149}\! \left(x , y\right)\\
F_{146}\! \left(x , y\right) &= F_{147}\! \left(x , y\right)\\
F_{147}\! \left(x , y\right) &= F_{148}\! \left(x , y\right) F_{17}\! \left(x , y\right)\\
F_{148}\! \left(x , y\right) &= F_{146}\! \left(x , y\right)+F_{16}\! \left(x , y\right)\\
F_{149}\! \left(x , y\right) &= F_{150}\! \left(x , y\right)+F_{157}\! \left(x , y\right)\\
F_{150}\! \left(x , y\right) &= F_{151}\! \left(x , y\right)\\
F_{151}\! \left(x , y\right) &= F_{152}\! \left(x , y\right) F_{17}\! \left(x , y\right)\\
F_{152}\! \left(x , y\right) &= F_{153}\! \left(x , y\right)+F_{154}\! \left(x , y\right)\\
F_{153}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{17}\! \left(x , y\right)\\
F_{154}\! \left(x , y\right) &= F_{150}\! \left(x , y\right)+F_{155}\! \left(x , y\right)\\
F_{155}\! \left(x , y\right) &= F_{156}\! \left(x , y\right)\\
F_{156}\! \left(x , y\right) &= F_{150}\! \left(x , y\right) F_{17}\! \left(x , y\right)\\
F_{157}\! \left(x , y\right) &= F_{158}\! \left(x , y\right)+F_{167}\! \left(x , y\right)+F_{19}\! \left(x \right)\\
F_{158}\! \left(x , y\right) &= F_{159}\! \left(x , y\right) F_{17}\! \left(x , y\right)\\
F_{159}\! \left(x , y\right) &= F_{160}\! \left(x , y\right)+F_{161}\! \left(x , y\right)\\
F_{160}\! \left(x , y\right) &= F_{13}\! \left(x , y\right)+F_{18}\! \left(x , y\right)\\
F_{161}\! \left(x , y\right) &= F_{157}\! \left(x , y\right)+F_{162}\! \left(x , y\right)\\
F_{162}\! \left(x , y\right) &= 2 F_{19}\! \left(x \right)+F_{163}\! \left(x , y\right)+F_{164}\! \left(x , y\right)\\
F_{163}\! \left(x , y\right) &= F_{157}\! \left(x , y\right) F_{17}\! \left(x , y\right)\\
F_{164}\! \left(x , y\right) &= F_{165}\! \left(x , y\right) F_{17}\! \left(x , y\right)\\
F_{165}\! \left(x , y\right) &= F_{166}\! \left(x , y\right)\\
F_{166}\! \left(x , y\right) &= F_{155}\! \left(x , y\right)+F_{162}\! \left(x , y\right)\\
F_{167}\! \left(x , y\right) &= F_{168}\! \left(x , y\right) F_{17}\! \left(x , y\right)\\
F_{168}\! \left(x , y\right) &= F_{149}\! \left(x , y\right)+F_{169}\! \left(x , y\right)\\
F_{169}\! \left(x , y\right) &= F_{170}\! \left(x , y\right)+F_{175}\! \left(x , y\right)\\
F_{170}\! \left(x , y\right) &= F_{156}\! \left(x , y\right)+F_{171}\! \left(x , y\right)+F_{19}\! \left(x \right)\\
F_{171}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{172}\! \left(x , y\right)\\
F_{172}\! \left(x , y\right) &= F_{173}\! \left(x , y\right)+F_{174}\! \left(x , y\right)\\
F_{173}\! \left(x , y\right) &= F_{17}\! \left(x , y\right)\\
F_{174}\! \left(x , y\right) &= F_{155}\! \left(x , y\right)\\
F_{175}\! \left(x , y\right) &= F_{163}\! \left(x , y\right)+F_{176}\! \left(x , y\right)+F_{180}\! \left(x , y\right)+F_{19}\! \left(x \right)\\
F_{176}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{177}\! \left(x , y\right)\\
F_{177}\! \left(x , y\right) &= F_{178}\! \left(x , y\right)+F_{179}\! \left(x , y\right)\\
F_{178}\! \left(x , y\right) &= F_{18}\! \left(x , y\right)\\
F_{179}\! \left(x , y\right) &= F_{162}\! \left(x , y\right)\\
F_{180}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{181}\! \left(x , y\right)\\
F_{181}\! \left(x , y\right) &= F_{169}\! \left(x , y\right)\\
F_{182}\! \left(x , y\right) &= F_{183}\! \left(x , y\right)\\
F_{183}\! \left(x , y\right) &= F_{184}\! \left(x , y\right) F_{29}\! \left(x \right) F_{4}\! \left(x \right) F_{46}\! \left(x \right)\\
F_{184}\! \left(x , y\right) &= F_{140}\! \left(x , y\right)+F_{185}\! \left(x , y\right)\\
F_{185}\! \left(x , y\right) &= F_{186}\! \left(x , y\right) F_{30}\! \left(x \right)\\
F_{186}\! \left(x , y\right) &= F_{187}\! \left(x , y\right)+F_{190}\! \left(x , y\right)\\
F_{187}\! \left(x , y\right) &= F_{188}\! \left(x , y\right)\\
F_{188}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{189}\! \left(x , y\right)\\
F_{189}\! \left(x , y\right) &= F_{12}\! \left(x , y\right)+F_{149}\! \left(x , y\right)\\
F_{190}\! \left(x , y\right) &= F_{187}\! \left(x , y\right) F_{89}\! \left(x , y\right)\\
F_{191}\! \left(x , y\right) &= F_{192}\! \left(x , y\right)+F_{195}\! \left(x , y\right)\\
F_{192}\! \left(x , y\right) &= F_{193}\! \left(x , y\right)+F_{194}\! \left(x , y\right)\\
F_{193}\! \left(x , y\right) &= F_{2}\! \left(x \right) F_{88}\! \left(x , y\right)\\
F_{194}\! \left(x , y\right) &= F_{143}\! \left(x , y\right) F_{31}\! \left(x \right)\\
F_{195}\! \left(x , y\right) &= F_{196}\! \left(x , y\right)\\
F_{196}\! \left(x , y\right) &= F_{197}\! \left(x , y\right) F_{29}\! \left(x \right) F_{4}\! \left(x \right) F_{46}\! \left(x \right)\\
F_{197}\! \left(x , y\right) &= F_{192}\! \left(x , y\right)+F_{198}\! \left(x , y\right)\\
F_{198}\! \left(x , y\right) &= F_{186}\! \left(x , y\right) F_{31}\! \left(x \right)\\
F_{199}\! \left(x , y\right) &= F_{200}\! \left(x , y\right)+F_{202}\! \left(x , y\right)\\
F_{200}\! \left(x , y\right) &= F_{2}\! \left(x \right)+F_{201}\! \left(x , y\right)\\
F_{7}\! \left(x , y\right) &= F_{187}\! \left(x , y\right)+F_{201}\! \left(x , y\right)\\
F_{202}\! \left(x , y\right) &= F_{203}\! \left(x , y\right)\\
F_{203}\! \left(x , y\right) &= F_{204}\! \left(x , y\right) F_{29}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{204}\! \left(x , y\right) &= F_{205}\! \left(x , y\right)+F_{211}\! \left(x , y\right)\\
F_{205}\! \left(x , y\right) &= F_{199}\! \left(x , y\right)+F_{206}\! \left(x , y\right)\\
F_{207}\! \left(x , y\right) &= F_{186}\! \left(x , y\right)+F_{206}\! \left(x , y\right)\\
F_{207}\! \left(x , y\right) &= F_{208}\! \left(x , y\right)+F_{210}\! \left(x , y\right)\\
F_{208}\! \left(x , y\right) &= F_{142}\! \left(x , y\right)+F_{209}\! \left(x , y\right)\\
F_{209}\! \left(x , y\right) &= F_{0}\! \left(x \right) F_{89}\! \left(x , y\right)\\
F_{210}\! \left(x , y\right) &= F_{7}\! \left(x , y\right) F_{89}\! \left(x , y\right)\\
F_{211}\! \left(x , y\right) &= F_{200}\! \left(x , y\right)+F_{212}\! \left(x , y\right)\\
F_{212}\! \left(x , y\right) &= -\frac{-F_{213}\! \left(x , y\right)+F_{213}\! \left(x , 1\right)}{-1+y}\\
F_{213}\! \left(x , y\right) &= F_{194}\! \left(x , y\right)+F_{214}\! \left(x , y\right)\\
F_{214}\! \left(x , y\right) &= F_{2}\! \left(x \right) F_{89}\! \left(x , y\right)\\
F_{215}\! \left(x , y\right) &= F_{216}\! \left(x , y\right)\\
F_{216}\! \left(x , y\right) &= F_{217}\! \left(x , y\right) F_{4}\! \left(x \right)\\
F_{217}\! \left(x , y\right) &= F_{218}\! \left(x \right)+F_{222}\! \left(x , y\right)\\
F_{218}\! \left(x \right) &= \frac{F_{219}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{219}\! \left(x \right) &= F_{220}\! \left(x \right)\\
F_{220}\! \left(x \right) &= F_{221}\! \left(x , 1\right)\\
F_{221}\! \left(x , y\right) &= F_{7}\! \left(x , y\right)+F_{98}\! \left(x , y\right)\\
F_{222}\! \left(x , y\right) &= F_{223}\! \left(x , y\right)\\
F_{223}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{224}\! \left(x , y\right)\\
F_{224}\! \left(x , y\right) &= F_{225}\! \left(x , y\right)+F_{227}\! \left(x , y\right)\\
F_{225}\! \left(x , y\right) &= F_{226}\! \left(x , y\right) F_{46}\! \left(x \right)\\
F_{226}\! \left(x , y\right) &= -\frac{-F_{126}\! \left(x , y\right) y +F_{126}\! \left(x , 1\right)}{-1+y}\\
F_{227}\! \left(x , y\right) &= -\frac{-y F_{132}\! \left(x , y\right)+F_{132}\! \left(x , 1\right)}{-1+y}\\
F_{228}\! \left(x \right) &= F_{10}\! \left(x , 1\right)\\
F_{229}\! \left(x , y\right) &= F_{125}\! \left(x , y\right) F_{46}\! \left(x \right)\\
\end{align*}\)