01324_01342_03124_03142_03214_30124_30142_30214
Counting sequence:
1, 1, 2, 6, 24, 112, 562, 2929, 15644, 85118, 470102, 2628610, 14850318, 84629427, 485884092, 2807588907, 16314491056, 95272262896, 558823787084, 3290782081659, 19447761472436, 115303109294524, 685626776182658, 4087903783179805, 24433411437158122, 146370624992810342, 878689853559687020, 5285217634710003702, 31847583246985952522, 192230930578956817425, 1162131681501970426744, 7036057700722056059640, 42658554215413003908392, 258970205595005080018314, 1574083472610620418389406, 9578778405065822335528692, 58353845859367817010238298, 355861172401502420090874266, 2172302134991851133736142542, 13272931664799518773143114860, 81170942017364294872018217628, 496824427188038281474329999434, 3043383979172408749783152926696, 18657180958279040996463884948291, 114460554260652400405882446440474, 702703755793336984746120770380213, 4317002218028646205488128947382618, 26538331391191538567833590493427282, 163243097766040670955890935739349334, 1004743340316299891831842617452008455, 6187630856416731598193796549778154650, 38127036743568792859392275959605571525, 235056406683639301485695879091831898464, 1449883159036589158415362962140008787349, 8947624405741799258409329795590756656454, 55244455764498592006585406310284949785953, 341246853506901843574967080240867925775514, 2108826135264954316665435158080879072899638, 13037627486470963996756188134049263915563622, 80637279739550523846496445226795462846185961, 498938267384518224529918324173787636872867570, 3088345127919866789017988832503755306709774291, 19123509447410841449931772947294735626645569518, 118458724576013543462306253837121457166160019452, 734039397809812809525514772682752472676057476680, 4550089483182089548640064575132347536212398870224, 28213979741487417277940038641371981849844185745770, 175004170082318001206349633975347067592072151221295, 1085845539921389106675116293227559999131904849169508, 6739372452880856444310840595588210751155847543375678, 41840698356106552586233691500652186977234362247146754, 259838147743573596969322940524169945402192548691987514, 1614091036902040149397498371574855514281130835239588594, 10029308971889158680241111616026968049597991217392208130, 62334537292215306351888386213463523755350808489409659878, 387523648640487487056089469194970072082172123636095920900, 2409775227578224051945496115985362540927634389535823467494, 14988595503266288817419349787772841065530028477765879760582, 93249980936105125330640374332166396984875662606827098526878, 580279731589770737177644366549404509730321850243397010221997, 3611805983218008803119461133495926908947806995031775760350852, 22485751205588683544036033043348724869980030510716700507802592, 140018063200409335419167823447792566818789207628482978908438838, 872071693905718134295495391984037366047974800179836422467298432, 5432623828198531697251967520144602031986298625291390414127727376, 33849661710758970287831493809789546684029633986449211471072534628, 210952313092750794769836612431792687141473478092779532879066985860, 1314914712935704829325451575597573337273336098710696413352250604973, 8197706214724946000121999636032758382315556073539190614176533323542, 51117168369681259789543242636173115997504438844202365809185764618814, 318800620328144607180920791973599225229484093559766976203064231132136, 1988601556818771402122692434252047321354216700734352986628833362729081, 12406549423804476946825995548185335869440140300364530520972165419440698, 77415386132631745914518399764477641685087363022991210138283534954621633, 483142307895215479708152454224745447045922039216184372855350542607103350, 3015732974834750355019758896996019336541674245864219857047279658124720630, 18826920752335469009813562606370208397136236281170429994545890147443836798, 117552780891782201508252437229554165452570379935779996553866168353260100050, 734095182469306832206869836658820091711791414533073359294635275376784789560, 4584968801992549230765930189152463212065365188633923059510595989384717302983, 28640702733753983946460918562854917655010792227802719572081492909260884458322
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://www.permpal.com/tree/24155/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]*F[7,x]
F[3,x] = F[4,x,1]
F[4,x,k[0]] = F[1,x]+F[5,x,k[0]]+F[8,x,k[0]]
F[5,x,k[0]] = F[6,x,k[0]]*F[7,x]
F[6,x,k[0]] = 1/(-1+k[0])*(F[4,x,k[0]]*k[0]-F[4,x,1])
F[7,x] = x
F[8,x,k[0]] = F[21,x,k[0]]*F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,1,k[0]]
F[10,x,k[0],k[1]] = F[11,x,k[0]*k[1],k[1]]
F[11,x,k[0],k[1]] = F[1,x]+F[12,x,k[0],k[1]]+F[27,x,k[0],k[1]]+F[57,x,k[0],k[1]]
F[12,x,k[0],k[1]] = F[13,x,k[0],k[1]]*F[7,x]
F[13,x,k[0],k[1]] = F[14,x,1,k[0],k[1]]
F[14,x,k[0],k[1],k[2]] = F[1,x]+F[15,x,k[0],k[1],k[2]]+F[17,x,k[0],k[1],k[2]]+F[22,x,k[0],k[1],k[2]]+F[54,x,k[0],k[1],k[2]]
F[15,x,k[0],k[1],k[2]] = F[16,x,k[0],k[1],k[2]]*F[7,x]
F[16,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[14,x,k[0],k[1],k[2]]*k[0]-F[14,x,1,k[1],k[2]])
F[17,x,k[0],k[1],k[2]] = F[18,x,k[0],k[1],k[2]]*F[21,x,k[0]]
F[18,x,k[0],k[1],k[2]] = (F[19,x,k[0],k[1]]*k[1]-F[19,x,k[0],k[2]]*k[2])/(-k[2]+k[1])
F[19,x,k[0],k[1]] = (F[20,x,k[0],1]*k[0]-F[20,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[20,x,k[0],k[1]] = F[11,x,k[0],k[0]*k[1]]
F[21,x,k[0]] = k[0]*x
F[22,x,k[0],k[1],k[2]] = F[21,x,k[1]]*F[23,x,k[0],k[1],k[2]]
F[23,x,k[0],k[1],k[2]] = (-F[24,x,1,k[1],k[2]]*k[1]+F[24,x,k[0]/k[1],k[1],k[2]]*k[0])/(-k[1]+k[0])
F[24,x,k[0],k[1],k[2]] = F[1,x]+F[25,x,k[0],k[1]]+F[26,x,k[0],k[1]]+F[29,x,k[0],k[1],k[2]]+F[52,x,k[0],k[1],k[2]]
F[25,x,k[0],k[1]] = F[12,x,k[0]*k[1],k[1]]
F[26,x,k[0],k[1]] = F[27,x,k[0]*k[1],k[1]]
F[27,x,k[0],k[1]] = F[21,x,k[0]]*F[28,x,k[0],k[1]]
F[28,x,k[0],k[1]] = F[24,x,1,k[0],k[1]]
F[29,x,k[0],k[1],k[2]] = F[30,x,k[0],k[1],k[2]]
F[30,x,k[0],k[1],k[2]] = F[21,x,k[1]]*F[31,x,k[1]]*F[34,x,k[1],k[2]]*F[4,x,k[1]]
F[31,x,k[0]] = F[1,x]+F[32,x,k[0]]
F[32,x,k[0]] = F[33,x,k[0]]
F[33,x,k[0]] = F[21,x,k[0]]*F[31,x,k[0]]
F[35,x,k[0],k[1]] = F[21,x,k[0]]*F[3,x]*F[31,x,k[0]]*F[34,x,k[0],k[1]]
F[35,x,k[0],k[1]] = F[36,x,k[0],k[1]]
F[37,x,k[0],k[1]] = F[1,x]+F[36,x,k[0],k[1]]+F[39,x,k[0],k[1]]+F[42,x,k[0],k[1]]+F[45,x,k[0],k[1]]
F[37,x,k[0],k[1]] = (F[38,x,k[0]]*k[0]-F[38,x,k[1]]*k[1])/(-k[1]+k[0])
F[38,x,k[0]] = F[11,x,1,k[0]]
F[39,x,k[0],k[1]] = F[40,x,k[0],k[1]]*F[7,x]
F[40,x,k[0],k[1]] = (F[41,x,k[0]]*k[0]-F[41,x,k[1]]*k[1])/(-k[1]+k[0])
F[41,x,k[0]] = F[13,x,1,k[0]]
F[42,x,k[0],k[1]] = F[43,x,k[0],k[1]]*F[7,x]
F[43,x,k[0],k[1]] = (F[44,x,k[0]]*k[0]-F[44,x,k[1]]*k[1])/(-k[1]+k[0])
F[44,x,k[0]] = F[28,x,1,k[0]]
F[45,x,k[0],k[1]] = F[46,x,k[0],k[1]]
F[46,x,k[0],k[1]] = F[21,x,k[1]]*F[3,x]*F[31,x,k[0]]*F[31,x,k[1]]*F[47,x,k[1]]
F[47,x,k[0]] = F[1,x]+F[48,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]
F[49,x,k[0]] = F[21,x,k[0]]*F[50,x,k[0]]
F[50,x,k[0]] = F[47,x,k[0]]+F[51,x,k[0]]
F[51,x,k[0]] = F[48,x,k[0]]
F[52,x,k[0],k[1],k[2]] = F[53,x,k[0],k[1],k[2]]
F[53,x,k[0],k[1],k[2]] = F[21,x,k[2]]*F[31,x,k[1]]*F[31,x,k[2]]*F[4,x,k[1]]*F[47,x,k[2]]
F[54,x,k[0],k[1],k[2]] = F[55,x,k[0],k[1],k[2]]
F[55,x,k[0],k[1],k[2]] = F[21,x,k[2]]*F[31,x,k[2]]*F[47,x,k[2]]*F[56,x,k[0],k[1]]
F[56,x,k[0],k[1]] = (F[4,x,k[0]]*k[0]-F[4,x,k[1]]*k[1])/(-k[1]+k[0])
F[57,x,k[0],k[1]] = F[58,x,k[0],k[1]]
F[58,x,k[0],k[1]] = F[21,x,k[1]]*F[31,x,k[1]]*F[4,x,k[0]]*F[47,x,k[1]]
System of equations in latex syntax:
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_{7}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x , 1\right)
F_{4}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{5}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)
F_{5}\! \left(x , y_{0}\right) = F_{6}\! \left(x , y_{0}\right) F_{7}\! \left(x \right)
F_{6}\! \left(x , y_{0}\right) = \frac{y_{0} F_{4}\! \left(x , y_{0}\right)-F_{4}\! \left(x , 1\right)}{-1+y_{0}}
F_{7}\! \left(x \right) = x
F_{8}\! \left(x , y_{0}\right) = F_{21}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)
F_{9}\! \left(x , y_{0}\right) = F_{10}\! \left(x , 1, y_{0}\right)
F_{10}\! \left(x , y_{0}, y_{1}\right) = F_{11}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{11}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y_{0}, y_{1}\right)+F_{27}\! \left(x , y_{0}, y_{1}\right)+F_{57}\! \left(x , y_{0}, y_{1}\right)
F_{12}\! \left(x , y_{0}, y_{1}\right) = F_{13}\! \left(x , y_{0}, y_{1}\right) F_{7}\! \left(x \right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , 1, y_{0}, y_{1}\right)
F_{14}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{54}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{7}\! \left(x \right)
F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{0} F_{14}\! \left(x , y_{0}, y_{1}, y_{2}\right)-F_{14}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{21}\! \left(x , y_{0}\right)
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{1} F_{19}\! \left(x , y_{0}, y_{1}\right)-y_{2} F_{19}\! \left(x , y_{0}, y_{2}\right)}{-y_{2}+y_{1}}
F_{19}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{20}\! \left(x , y_{0}, 1\right)-y_{1} F_{20}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)}{-y_{1}+y_{0}}
F_{20}\! \left(x , y_{0}, y_{1}\right) = F_{11}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{21}\! \left(x , y_{0}\right) = y_{0} x
F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{1}\right) F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{-y_{1} F_{24}\! \left(x , 1, y_{1}, y_{2}\right)+y_{0} F_{24}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}, y_{2}\right)}{-y_{1}+y_{0}}
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{25}\! \left(x , y_{0}, y_{1}\right)+F_{26}\! \left(x , y_{0}, y_{1}\right)+F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{52}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{25}\! \left(x , y_{0}, y_{1}\right) = F_{12}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{26}\! \left(x , y_{0}, y_{1}\right) = F_{27}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{27}\! \left(x , y_{0}, y_{1}\right) = F_{21}\! \left(x , y_{0}\right) F_{28}\! \left(x , y_{0}, y_{1}\right)
F_{28}\! \left(x , y_{0}, y_{1}\right) = F_{24}\! \left(x , 1, y_{0}, y_{1}\right)
F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{1}\right) F_{31}\! \left(x , y_{1}\right) F_{34}\! \left(x , y_{1}, y_{2}\right) F_{4}\! \left(x , y_{1}\right)
F_{31}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{32}\! \left(x , y_{0}\right)
F_{32}\! \left(x , y_{0}\right) = F_{33}\! \left(x , y_{0}\right)
F_{33}\! \left(x , y_{0}\right) = F_{21}\! \left(x , y_{0}\right) F_{31}\! \left(x , y_{0}\right)
F_{35}\! \left(x , y_{0}, y_{1}\right) = F_{21}\! \left(x , y_{0}\right) F_{3}\! \left(x \right) F_{31}\! \left(x , y_{0}\right) F_{34}\! \left(x , y_{0}, y_{1}\right)
F_{35}\! \left(x , y_{0}, y_{1}\right) = F_{36}\! \left(x , y_{0}, y_{1}\right)
F_{37}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{36}\! \left(x , y_{0}, y_{1}\right)+F_{39}\! \left(x , y_{0}, y_{1}\right)+F_{42}\! \left(x , y_{0}, y_{1}\right)+F_{45}\! \left(x , y_{0}, y_{1}\right)
F_{37}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{38}\! \left(x , y_{0}\right)-y_{1} F_{38}\! \left(x , y_{1}\right)}{-y_{1}+y_{0}}
F_{38}\! \left(x , y_{0}\right) = F_{11}\! \left(x , 1, y_{0}\right)
F_{39}\! \left(x , y_{0}, y_{1}\right) = F_{40}\! \left(x , y_{0}, y_{1}\right) F_{7}\! \left(x \right)
F_{40}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{41}\! \left(x , y_{0}\right)-y_{1} F_{41}\! \left(x , y_{1}\right)}{-y_{1}+y_{0}}
F_{41}\! \left(x , y_{0}\right) = F_{13}\! \left(x , 1, y_{0}\right)
F_{42}\! \left(x , y_{0}, y_{1}\right) = F_{43}\! \left(x , y_{0}, y_{1}\right) F_{7}\! \left(x \right)
F_{43}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{44}\! \left(x , y_{0}\right)-y_{1} F_{44}\! \left(x , y_{1}\right)}{-y_{1}+y_{0}}
F_{44}\! \left(x , y_{0}\right) = F_{28}\! \left(x , 1, y_{0}\right)
F_{45}\! \left(x , y_{0}, y_{1}\right) = F_{46}\! \left(x , y_{0}, y_{1}\right)
F_{46}\! \left(x , y_{0}, y_{1}\right) = F_{21}\! \left(x , y_{1}\right) F_{3}\! \left(x \right) F_{31}\! \left(x , y_{0}\right) F_{31}\! \left(x , y_{1}\right) F_{47}\! \left(x , y_{1}\right)
F_{47}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{48}\! \left(x , y_{0}\right)
F_{48}\! \left(x , y_{0}\right) = F_{49}\! \left(x , y_{0}\right)
F_{49}\! \left(x , y_{0}\right) = F_{21}\! \left(x , y_{0}\right) F_{50}\! \left(x , y_{0}\right)
F_{50}\! \left(x , y_{0}\right) = F_{47}\! \left(x , y_{0}\right)+F_{51}\! \left(x , y_{0}\right)
F_{51}\! \left(x , y_{0}\right) = F_{48}\! \left(x , y_{0}\right)
F_{52}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{53}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{53}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{2}\right) F_{31}\! \left(x , y_{1}\right) F_{31}\! \left(x , y_{2}\right) F_{4}\! \left(x , y_{1}\right) F_{47}\! \left(x , y_{2}\right)
F_{54}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{55}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{55}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{2}\right) F_{31}\! \left(x , y_{2}\right) F_{47}\! \left(x , y_{2}\right) F_{56}\! \left(x , y_{0}, y_{1}\right)
F_{56}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{4}\! \left(x , y_{0}\right)-y_{1} F_{4}\! \left(x , y_{1}\right)}{-y_{1}+y_{0}}
F_{57}\! \left(x , y_{0}, y_{1}\right) = F_{58}\! \left(x , y_{0}, y_{1}\right)
F_{58}\! \left(x , y_{0}, y_{1}\right) = F_{21}\! \left(x , y_{1}\right) F_{31}\! \left(x , y_{1}\right) F_{4}\! \left(x , y_{0}\right) F_{47}\! \left(x , y_{1}\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x)*F_7(x))
Eq(F_3(x), F_4(x, 1))
Eq(F_4(x, k_0), F_1(x) + F_5(x, k_0) + F_8(x, k_0))
Eq(F_5(x, k_0), F_6(x, k_0)*F_7(x))
Eq(F_6(x, k_0), (k_0*F_4(x, k_0) - F_4(x, 1))/(k_0 - 1))
Eq(F_7(x), x)
Eq(F_8(x, k_0), F_21(x, k_0)*F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, 1, k_0))
Eq(F_10(x, k_0, k_1), F_11(x, k_0*k_1, k_1))
Eq(F_11(x, k_0, k_1), F_1(x) + F_12(x, k_0, k_1) + F_27(x, k_0, k_1) + F_57(x, k_0, k_1))
Eq(F_12(x, k_0, k_1), F_13(x, k_0, k_1)*F_7(x))
Eq(F_13(x, k_0, k_1), F_14(x, 1, k_0, k_1))
Eq(F_14(x, k_0, k_1, k_2), F_1(x) + F_15(x, k_0, k_1, k_2) + F_17(x, k_0, k_1, k_2) + F_22(x, k_0, k_1, k_2) + F_54(x, k_0, k_1, k_2))
Eq(F_15(x, k_0, k_1, k_2), F_16(x, k_0, k_1, k_2)*F_7(x))
Eq(F_16(x, k_0, k_1, k_2), (k_0*F_14(x, k_0, k_1, k_2) - F_14(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_17(x, k_0, k_1, k_2), F_18(x, k_0, k_1, k_2)*F_21(x, k_0))
Eq(F_18(x, k_0, k_1, k_2), (-k_1*F_19(x, k_0, k_1) + k_2*F_19(x, k_0, k_2))/(-k_1 + k_2))
Eq(F_19(x, k_0, k_1), (-k_0*F_20(x, k_0, 1) + k_1*F_20(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_20(x, k_0, k_1), F_11(x, k_0, k_0*k_1))
Eq(F_21(x, k_0), k_0*x)
Eq(F_22(x, k_0, k_1, k_2), F_21(x, k_1)*F_23(x, k_0, k_1, k_2))
Eq(F_23(x, k_0, k_1, k_2), (-k_0*F_24(x, k_0/k_1, k_1, k_2) + k_1*F_24(x, 1, k_1, k_2))/(-k_0 + k_1))
Eq(F_24(x, k_0, k_1, k_2), F_1(x) + F_25(x, k_0, k_1) + F_26(x, k_0, k_1) + F_29(x, k_0, k_1, k_2) + F_52(x, k_0, k_1, k_2))
Eq(F_25(x, k_0, k_1), F_12(x, k_0*k_1, k_1))
Eq(F_26(x, k_0, k_1), F_27(x, k_0*k_1, k_1))
Eq(F_27(x, k_0, k_1), F_21(x, k_0)*F_28(x, k_0, k_1))
Eq(F_28(x, k_0, k_1), F_24(x, 1, k_0, k_1))
Eq(F_29(x, k_0, k_1, k_2), F_30(x, k_0, k_1, k_2))
Eq(F_30(x, k_0, k_1, k_2), F_21(x, k_1)*F_31(x, k_1)*F_34(x, k_1, k_2)*F_4(x, k_1))
Eq(F_31(x, k_0), F_1(x) + F_32(x, k_0))
Eq(F_32(x, k_0), F_33(x, k_0))
Eq(F_33(x, k_0), F_21(x, k_0)*F_31(x, k_0))
Eq(F_35(x, k_0, k_1), F_21(x, k_0)*F_3(x)*F_31(x, k_0)*F_34(x, k_0, k_1))
Eq(F_35(x, k_0, k_1), F_36(x, k_0, k_1))
Eq(F_37(x, k_0, k_1), F_1(x) + F_36(x, k_0, k_1) + F_39(x, k_0, k_1) + F_42(x, k_0, k_1) + F_45(x, k_0, k_1))
Eq(F_37(x, k_0, k_1), (-k_0*F_38(x, k_0) + k_1*F_38(x, k_1))/(-k_0 + k_1))
Eq(F_38(x, k_0), F_11(x, 1, k_0))
Eq(F_39(x, k_0, k_1), F_40(x, k_0, k_1)*F_7(x))
Eq(F_40(x, k_0, k_1), (-k_0*F_41(x, k_0) + k_1*F_41(x, k_1))/(-k_0 + k_1))
Eq(F_41(x, k_0), F_13(x, 1, k_0))
Eq(F_42(x, k_0, k_1), F_43(x, k_0, k_1)*F_7(x))
Eq(F_43(x, k_0, k_1), (-k_0*F_44(x, k_0) + k_1*F_44(x, k_1))/(-k_0 + k_1))
Eq(F_44(x, k_0), F_28(x, 1, k_0))
Eq(F_45(x, k_0, k_1), F_46(x, k_0, k_1))
Eq(F_46(x, k_0, k_1), F_21(x, k_1)*F_3(x)*F_31(x, k_0)*F_31(x, k_1)*F_47(x, k_1))
Eq(F_47(x, k_0), F_1(x) + F_48(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0))
Eq(F_49(x, k_0), F_21(x, k_0)*F_50(x, k_0))
Eq(F_50(x, k_0), F_47(x, k_0) + F_51(x, k_0))
Eq(F_51(x, k_0), F_48(x, k_0))
Eq(F_52(x, k_0, k_1, k_2), F_53(x, k_0, k_1, k_2))
Eq(F_53(x, k_0, k_1, k_2), F_21(x, k_2)*F_31(x, k_1)*F_31(x, k_2)*F_4(x, k_1)*F_47(x, k_2))
Eq(F_54(x, k_0, k_1, k_2), F_55(x, k_0, k_1, k_2))
Eq(F_55(x, k_0, k_1, k_2), F_21(x, k_2)*F_31(x, k_2)*F_47(x, k_2)*F_56(x, k_0, k_1))
Eq(F_56(x, k_0, k_1), (-k_0*F_4(x, k_0) + k_1*F_4(x, k_1))/(-k_0 + k_1))
Eq(F_57(x, k_0, k_1), F_58(x, k_0, k_1))
Eq(F_58(x, k_0, k_1), F_21(x, k_1)*F_31(x, k_1)*F_4(x, k_0)*F_47(x, k_1))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "row_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 3, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[4, 1]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[5, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[4, 0]]}, {"patt": [0], "pos": [[5, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [3, 1], [4, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [3, 1], [5, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [4, 1], [4, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [4, 1], [5, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [5, 1], [5, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [3, 1], [4, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [3, 1], [5, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [4, 1], [4, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [4, 1], [5, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [5, 1], [5, 1]]}, {"patt": [1, 0, 2], "pos": [[3, 1], [3, 1], [4, 1]]}, {"patt": [1, 0, 2], "pos": [[3, 1], [3, 1], [5, 1]]}, {"patt": [1, 0, 2], "pos": [[3, 1], [4, 1], [4, 1]]}, {"patt": [1, 0, 2], "pos": [[3, 1], [4, 1], [5, 1]]}, {"patt": [1, 0, 2], "pos": [[3, 1], [5, 1], [5, 1]]}, {"patt": [1, 0, 2], "pos": [[4, 1], [4, 1], [4, 1]]}, {"patt": [1, 0, 2], "pos": [[4, 1], [4, 1], [5, 1]]}, {"patt": [1, 0, 2], "pos": [[4, 1], [5, 1], [5, 1]]}, {"patt": [1, 0, 2], "pos": [[5, 1], [5, 1], [5, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [4, 1], [4, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [4, 1], [5, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [5, 1], [5, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [4, 1], [4, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [4, 1], [5, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [5, 1], [5, 1]]}, {"patt": [1, 2, 0], "pos": [[3, 1], [4, 1], [4, 1]]}, {"patt": [1, 2, 0], "pos": [[3, 1], [4, 1], [5, 1]]}, {"patt": [1, 2, 0], "pos": [[3, 1], [5, 1], [5, 1]]}, {"patt": [1, 2, 0], "pos": [[4, 1], [4, 1], [4, 1]]}, {"patt": [1, 2, 0], "pos": [[4, 1], [4, 1], [5, 1]]}, {"patt": [1, 2, 0], "pos": [[4, 1], [5, 1], [5, 1]]}, {"patt": [1, 2, 0], "pos": [[5, 1], [5, 1], [5, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 1], [2, 1], [2, 1], [3, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 1], [2, 1], [2, 1], [4, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 1], [2, 1], [2, 1], [5, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 1], [2, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [3, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [4, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [5, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 1], [3, 1], [4, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 1], [3, 1], [5, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [3, 1], [3, 1], [4, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [3, 1], [3, 1], [5, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[3, 1], [3, 1], [3, 1], [4, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[3, 1], [3, 1], [3, 1], [5, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [2, 1], [2, 1], [3, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [2, 1], [2, 1], [4, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [2, 1], [2, 1], [5, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [2, 1], [3, 1], [3, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[2, 1], [2, 1], [2, 1], [3, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[2, 1], [2, 1], [2, 1], [4, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[2, 1], [2, 1], [2, 1], [5, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[2, 1], [2, 1], [3, 1], [3, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[2, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [2, 1], [2, 1], [3, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [2, 1], [2, 1], [4, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [2, 1], [2, 1], [5, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [2, 1], [3, 1], [3, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [2, 1], [3, 1], [4, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [2, 1], [3, 1], [5, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [3, 1], [3, 1], [4, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [3, 1], [3, 1], [5, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [3, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [4, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [5, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 1], [2, 1], [3, 1], [3, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 1], [2, 1], [3, 1], [4, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 1], [2, 1], [3, 1], [5, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 1], [3, 1], [3, 1], [4, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 1], [3, 1], [3, 1], [5, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[3, 1], [3, 1], [3, 1], [4, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[3, 1], [3, 1], [3, 1], [5, 1]]}, {"patt": [2, 1, 0, 3], 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