0123_0132_0231_2013_3012
Counting sequence:
1, 1, 2, 6, 19, 59, 183, 578, 1873, 6224, 21132, 73013, 255843, 906834, 3244988, 11705418, 42516119, 155353811, 570658659, 2105999243, 7804616423, 29031830019, 108360621101, 405703860059, 1523250840807, 5733991413785, 21635996422435, 81818639024789, 310036684110351, 1177055343671273, 4476592725931191, 17053546278695214, 65065776553048661, 248610776984905380, 951215821956232688, 3644144736697063797, 13977779460532628359, 53675727097982782546, 206342345510723513372, 794044836980337032991, 3058618775416793112289, 11792569249761410058986, 45506653194380930065152, 175754607402922473341027, 679339914909106555695491, 2627849557919628133801704, 10172605684902817798636286, 39406567215166197866416607, 152755508111361438642777657, 592522745143828595904023948, 2299756019741363324135642330, 8931337111626099234437567979, 34705570340872738597700259191, 134933707350246942701349799478, 524893733912931067656673014516, 2042883431431240681165394218013, 7954796878579624119339616438181, 30989914897005634806297895189212, 120784252300277696182009040526470, 470968777847860415996052764567171, 1837212359052857243973019570584531, 7169781580932949341428747423334566, 27991489174036099767629900000230052, 109323633337740710392639037218657626, 427134655285145152984017800290900775, 1669449283031761410303259036559431187, 6527314210629637868854909555049605587, 25529604829082215803026725386532853075, 99884377836570559820031862281692147351, 390922582249695545416537486454861442315, 1530451789931976141853518404771841892517, 5993498686310574713581037812813543970807, 23478446818327487551674258612155271107535, 91998971972096032875740241329172402430901, 360593475997678892191987618664649763701095, 1413744045462745025418472190031264518139717, 5544196671318797815106234926242882001622687, 21747953028696222028658985077715493413463325, 85331068615720659233617574773405288126554171, 334890055749935867894712453386816361999256295, 1314622080572203370844274205973645641670099307, 5161793540318361974108090731289339680454129447, 20272107531254307253303826316720333623654680305, 79633050761315849070035443756208172982399260161, 312882800884036308185758571009071972110488813535, 1229593887219008168484399543872041423404557493747, 4833160637580734933968226017507600227663746317217, 19001515026614769424025799637050649421441134073565, 74718939727391570720032069660998865412307386691731, 293870990551728374688212448424635988013806880680755, 1156017520896363804371023269111800780036117140560697, 4548330334574478471123437478505437565049394529348357, 17898544798223366057013864883461166856108772122584535, 70446578313243438051861903213990464023875851074344831, 277317265848074005313291092633431128817003964981863445, 1091860517144782033785881901085832841389746374117272027, 4299610648214004890399887801498700714073071082200033127, 16934069248359090681722082721587609193794055153445205545, 66705605338439060213292410024486363371435361391190008131, 262803249723991537162870949127004132588118790628925981325, 1035535960034735824923903073501689379970926788148902581327
Generating function in Maple syntax:
1/2*((-x^3+4*x^2-3*x+1)*(1-4*x)^(1/2)+3*x^3-4*x^2+3*x-1)/x/(x-1)^3
Generating function in latex syntax:
\frac{\left(-x^{3}+4 x^{2}-3 x +1\right) \sqrt{1-4 x}+3 x^{3}-4 x^{2}+3 x -1}{2 x \left(x -1\right)^{3}}
Generating function in sympy syntax:
(3*x**3/2 - 2*x**2 + 3*x/2 + sqrt(1 - 4*x)*(-x**3 + 4*x**2 - 3*x + 1)/2 - 1/2)/(x*(x - 1)**3)
Implicit equation for the generating function in Maple syntax:
x*(x-1)^6*F(x)^2-(3*x^3-4*x^2+3*x-1)*(x-1)^3*F(x)+x^6-6*x^5+18*x^4-23*x^3+16*x^2-6*x+1 = 0
Implicit equation for the generating function in latex syntax:
x \left(x -1\right)^{6} F \! \left(x \right)^{2}-\left(3 x^{3}-4 x^{2}+3 x -1\right) \left(x -1\right)^{3} F \! \left(x \right)+x^{6}-6 x^{5}+18 x^{4}-23 x^{3}+16 x^{2}-6 x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 59
a(6) = 183
a(n+5) = 2*(1+2*n)/(n+6)*a(n)-3*(12+7*n)/(n+6)*a(n+1)+3*(26+11*n)/(n+6)*a(n+2)-(82+23*n)/(n+6)*a(n+3)+2*(19+4*n)/(n+6)*a(n+4)+2*(n+1)/(n+6), n >= 7
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 19
a \! \left(5\right) = 59
a \! \left(6\right) = 183
a \! \left(n +5\right) = \frac{2 \left(1+2 n \right) a \! \left(n \right)}{n +6}-\frac{3 \left(12+7 n \right) a \! \left(n +1\right)}{n +6}+\frac{3 \left(26+11 n \right) a \! \left(n +2\right)}{n +6}-\frac{\left(82+23 n \right) a \! \left(n +3\right)}{n +6}+\frac{2 \left(19+4 n \right) a \! \left(n +4\right)}{n +6}+\frac{2 n +2}{n +6}, \quad n \geq 7
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/21506/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[21,x]*F[3,x]
F[3,x] = F[1,x]+F[4,x]+F[93,x]
F[4,x] = F[21,x]*F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[1,x]+F[7,x,k[0]]+F[90,x,k[0]]+F[92,x,k[0]]
F[7,x,k[0]] = F[8,x,k[0]]
F[8,x,k[0]] = F[21,x]*F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]+F[89,x]
F[10,x,k[0]] = F[11,x,k[0]]+F[43,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]+F[16,x,k[0]]
F[12,x,k[0]] = F[1,x]+F[13,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]
F[14,x,k[0]] = F[12,x,k[0]]*F[15,x,k[0]]
F[15,x,k[0]] = k[0]*x
F[16,x,k[0]] = F[17,x]+F[31,x,k[0]]
F[17,x] = F[18,x]
F[18,x] = F[19,x]*F[21,x]
F[19,x] = F[20,x]+F[22,x]
F[20,x] = F[1,x]+F[21,x]
F[21,x] = x
F[22,x] = F[23,x]+F[26,x]
F[23,x] = F[24,x]
F[24,x] = F[21,x]*F[25,x]
F[25,x] = F[1,x]+F[23,x]
F[26,x] = F[27,x]+F[28,x]+F[30,x]
F[27,x] = 0
F[28,x] = F[21,x]*F[29,x]
F[29,x] = F[21,x]+F[26,x]
F[30,x] = F[21,x]*F[23,x]
F[31,x,k[0]] = F[27,x]+F[32,x,k[0]]+F[40,x,k[0]]
F[32,x,k[0]] = F[21,x]*F[33,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]+F[35,x,k[0]]
F[34,x,k[0]] = F[15,x,k[0]]
F[35,x,k[0]] = F[36,x,k[0]]
F[36,x,k[0]] = F[27,x]+F[37,x,k[0]]+F[39,x,k[0]]
F[37,x,k[0]] = F[21,x]*F[38,x,k[0]]
F[38,x,k[0]] = F[15,x,k[0]]+F[36,x,k[0]]
F[39,x,k[0]] = F[15,x,k[0]]*F[23,x]
F[40,x,k[0]] = F[15,x,k[0]]*F[41,x,k[0]]
F[41,x,k[0]] = F[23,x]+F[42,x,k[0]]
F[42,x,k[0]] = F[40,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]+F[60,x,k[0]]
F[44,x,k[0]] = F[45,x]+F[54,x,k[0]]
F[45,x] = F[46,x]
F[46,x] = F[21,x]*F[47,x]
F[47,x] = F[25,x]+F[48,x]
F[48,x] = F[45,x]+F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[21,x]*F[51,x]
F[51,x] = F[52,x]+F[53,x]
F[52,x] = F[23,x]
F[53,x] = F[49,x]
F[54,x,k[0]] = F[27,x]+F[55,x,k[0]]+F[59,x,k[0]]
F[55,x,k[0]] = F[21,x]*F[56,x,k[0]]
F[56,x,k[0]] = F[57,x,k[0]]+F[58,x,k[0]]
F[57,x,k[0]] = F[13,x,k[0]]
F[58,x,k[0]] = F[54,x,k[0]]
F[59,x,k[0]] = F[15,x,k[0]]*F[44,x,k[0]]
F[60,x,k[0]] = F[61,x]+F[76,x,k[0]]
F[61,x] = F[27,x]+F[62,x]+F[66,x]
F[62,x] = F[21,x]*F[63,x]
F[63,x] = F[64,x]+F[65,x]
F[64,x] = F[17,x]
F[65,x] = F[61,x]
F[66,x] = F[21,x]*F[67,x]
F[67,x] = F[68,x]+F[69,x]
F[68,x] = F[45,x]
F[69,x] = F[70,x]
F[70,x] = F[27,x]+F[71,x]+F[74,x]
F[71,x] = F[21,x]*F[72,x]
F[72,x] = F[52,x]+F[73,x]
F[73,x] = F[70,x]
F[74,x] = F[21,x]*F[75,x]
F[75,x] = F[45,x]+F[70,x]
F[76,x,k[0]] = F[27,x]+F[77,x,k[0]]+F[81,x,k[0]]+F[82,x,k[0]]
F[77,x,k[0]] = F[21,x]*F[78,x,k[0]]
F[78,x,k[0]] = F[79,x,k[0]]+F[80,x,k[0]]
F[79,x,k[0]] = F[31,x,k[0]]
F[80,x,k[0]] = F[76,x,k[0]]
F[81,x,k[0]] = 0
F[82,x,k[0]] = F[15,x,k[0]]*F[83,x,k[0]]
F[83,x,k[0]] = F[70,x]+F[84,x,k[0]]
F[84,x,k[0]] = 2*F[27,x]+F[82,x,k[0]]+F[85,x,k[0]]
F[85,x,k[0]] = F[21,x]*F[86,x,k[0]]
F[86,x,k[0]] = F[87,x,k[0]]+F[88,x,k[0]]
F[87,x,k[0]] = F[42,x,k[0]]
F[88,x,k[0]] = F[84,x,k[0]]
F[89,x] = F[25,x]^2*F[21,x]
F[90,x,k[0]] = F[21,x]*F[91,x,k[0]]
F[91,x,k[0]] = 1/(-1+k[0])*(F[6,x,k[0]]*k[0]-F[6,x,1])
F[92,x,k[0]] = F[15,x,k[0]]*F[6,x,k[0]]
F[93,x] = F[94,x]
F[94,x] = F[21,x]*F[95,x]
F[95,x] = F[89,x]+F[96,x]
F[96,x] = F[97,x]+F[98,x]
F[97,x] = F[1,x]+F[17,x]
F[98,x] = F[45,x]+F[61,x]
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_{21}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{93}\! \left(x \right)
F_{4}\! \left(x \right) = F_{21}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{7}\! \left(x , y\right)+F_{90}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{89}\! \left(x \right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{16}\! \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_{12}\! \left(x , y\right) F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = y x
F_{16}\! \left(x , y\right) = F_{17}\! \left(x \right)+F_{31}\! \left(x , y\right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{21}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{22}\! \left(x \right)
F_{20}\! \left(x \right) = F_{1}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = x
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{26}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{21}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{1}\! \left(x \right)+F_{23}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)+F_{30}\! \left(x \right)
F_{27}\! \left(x \right) = 0
F_{28}\! \left(x \right) = F_{21}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{21}\! \left(x \right)+F_{26}\! \left(x \right)
F_{30}\! \left(x \right) = F_{21}\! \left(x \right) F_{23}\! \left(x \right)
F_{31}\! \left(x , y\right) = F_{27}\! \left(x \right)+F_{32}\! \left(x , y\right)+F_{40}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)+F_{35}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{15}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{27}\! \left(x \right)+F_{37}\! \left(x , y\right)+F_{39}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{38}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{36}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{23}\! \left(x \right)
F_{40}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{23}\! \left(x \right)+F_{42}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{40}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)+F_{60}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x \right)+F_{54}\! \left(x , y\right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{21}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{25}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{45}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{21}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{53}\! \left(x \right)
F_{52}\! \left(x \right) = F_{23}\! \left(x \right)
F_{53}\! \left(x \right) = F_{49}\! \left(x \right)
F_{54}\! \left(x , y\right) = F_{27}\! \left(x \right)+F_{55}\! \left(x , y\right)+F_{59}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{57}\! \left(x , y\right)+F_{58}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{54}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{44}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{61}\! \left(x \right)+F_{76}\! \left(x , y\right)
F_{61}\! \left(x \right) = F_{27}\! \left(x \right)+F_{62}\! \left(x \right)+F_{66}\! \left(x \right)
F_{62}\! \left(x \right) = F_{21}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{65}\! \left(x \right)
F_{64}\! \left(x \right) = F_{17}\! \left(x \right)
F_{65}\! \left(x \right) = F_{61}\! \left(x \right)
F_{66}\! \left(x \right) = F_{21}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{69}\! \left(x \right)
F_{68}\! \left(x \right) = F_{45}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{27}\! \left(x \right)+F_{71}\! \left(x \right)+F_{74}\! \left(x \right)
F_{71}\! \left(x \right) = F_{21}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{52}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{70}\! \left(x \right)
F_{74}\! \left(x \right) = F_{21}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{45}\! \left(x \right)+F_{70}\! \left(x \right)
F_{76}\! \left(x , y\right) = F_{27}\! \left(x \right)+F_{77}\! \left(x , y\right)+F_{81}\! \left(x , y\right)+F_{82}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{79}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{31}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{76}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = 0
F_{82}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{70}\! \left(x \right)+F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = 2 F_{27}\! \left(x \right)+F_{82}\! \left(x , y\right)+F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{87}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{42}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{84}\! \left(x , y\right)
F_{89}\! \left(x \right) = F_{25} \left(x \right)^{2} F_{21}\! \left(x \right)
F_{90}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = \frac{y F_{6}\! \left(x , y\right)-F_{6}\! \left(x , 1\right)}{-1+y}
F_{92}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{6}\! \left(x , y\right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{21}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{89}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)+F_{98}\! \left(x \right)
F_{97}\! \left(x \right) = F_{1}\! \left(x \right)+F_{17}\! \left(x \right)
F_{98}\! \left(x \right) = F_{45}\! \left(x \right)+F_{61}\! \left(x \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_21(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_4(x) + F_93(x))
Eq(F_4(x), F_21(x)*F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_1(x) + F_7(x, k_0) + F_90(x, k_0) + F_92(x, k_0))
Eq(F_7(x, k_0), F_8(x, k_0))
Eq(F_8(x, k_0), F_21(x)*F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0) + F_89(x))
Eq(F_10(x, k_0), F_11(x, k_0) + F_43(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0) + F_16(x, k_0))
Eq(F_12(x, k_0), F_1(x) + F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0))
Eq(F_14(x, k_0), F_12(x, k_0)*F_15(x, k_0))
Eq(F_15(x, k_0), k_0*x)
Eq(F_16(x, k_0), F_17(x) + F_31(x, k_0))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)*F_21(x))
Eq(F_19(x), F_20(x) + F_22(x))
Eq(F_20(x), F_1(x) + F_21(x))
Eq(F_21(x), x)
Eq(F_22(x), F_23(x) + F_26(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_21(x)*F_25(x))
Eq(F_25(x), F_1(x) + F_23(x))
Eq(F_26(x), F_27(x) + F_28(x) + F_30(x))
Eq(F_27(x), 0)
Eq(F_28(x), F_21(x)*F_29(x))
Eq(F_29(x), F_21(x) + F_26(x))
Eq(F_30(x), F_21(x)*F_23(x))
Eq(F_31(x, k_0), F_27(x) + F_32(x, k_0) + F_40(x, k_0))
Eq(F_32(x, k_0), F_21(x)*F_33(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0) + F_35(x, k_0))
Eq(F_34(x, k_0), F_15(x, k_0))
Eq(F_35(x, k_0), F_36(x, k_0))
Eq(F_36(x, k_0), F_27(x) + F_37(x, k_0) + F_39(x, k_0))
Eq(F_37(x, k_0), F_21(x)*F_38(x, k_0))
Eq(F_38(x, k_0), F_15(x, k_0) + F_36(x, k_0))
Eq(F_39(x, k_0), F_15(x, k_0)*F_23(x))
Eq(F_40(x, k_0), F_15(x, k_0)*F_41(x, k_0))
Eq(F_41(x, k_0), F_23(x) + F_42(x, k_0))
Eq(F_42(x, k_0), F_40(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0) + F_60(x, k_0))
Eq(F_44(x, k_0), F_45(x) + F_54(x, k_0))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_21(x)*F_47(x))
Eq(F_47(x), F_25(x) + F_48(x))
Eq(F_48(x), F_45(x) + F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_21(x)*F_51(x))
Eq(F_51(x), F_52(x) + F_53(x))
Eq(F_52(x), F_23(x))
Eq(F_53(x), F_49(x))
Eq(F_54(x, k_0), F_27(x) + F_55(x, k_0) + F_59(x, k_0))
Eq(F_55(x, k_0), F_21(x)*F_56(x, k_0))
Eq(F_56(x, k_0), F_57(x, k_0) + F_58(x, k_0))
Eq(F_57(x, k_0), F_13(x, k_0))
Eq(F_58(x, k_0), F_54(x, k_0))
Eq(F_59(x, k_0), F_15(x, k_0)*F_44(x, k_0))
Eq(F_60(x, k_0), F_61(x) + F_76(x, k_0))
Eq(F_61(x), F_27(x) + F_62(x) + F_66(x))
Eq(F_62(x), F_21(x)*F_63(x))
Eq(F_63(x), F_64(x) + F_65(x))
Eq(F_64(x), F_17(x))
Eq(F_65(x), F_61(x))
Eq(F_66(x), F_21(x)*F_67(x))
Eq(F_67(x), F_68(x) + F_69(x))
Eq(F_68(x), F_45(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_27(x) + F_71(x) + F_74(x))
Eq(F_71(x), F_21(x)*F_72(x))
Eq(F_72(x), F_52(x) + F_73(x))
Eq(F_73(x), F_70(x))
Eq(F_74(x), F_21(x)*F_75(x))
Eq(F_75(x), F_45(x) + F_70(x))
Eq(F_76(x, k_0), F_27(x) + F_77(x, k_0) + F_81(x, k_0) + F_82(x, k_0))
Eq(F_77(x, k_0), F_21(x)*F_78(x, k_0))
Eq(F_78(x, k_0), F_79(x, k_0) + F_80(x, k_0))
Eq(F_79(x, k_0), F_31(x, k_0))
Eq(F_80(x, k_0), F_76(x, k_0))
Eq(F_81(x, k_0), 0)
Eq(F_82(x, k_0), F_15(x, k_0)*F_83(x, k_0))
Eq(F_83(x, k_0), F_70(x) + F_84(x, k_0))
Eq(F_84(x, k_0), 2*F_27(x) + F_82(x, k_0) + F_85(x, k_0))
Eq(F_85(x, k_0), F_21(x)*F_86(x, k_0))
Eq(F_86(x, k_0), F_87(x, k_0) + F_88(x, k_0))
Eq(F_87(x, k_0), F_42(x, k_0))
Eq(F_88(x, k_0), F_84(x, k_0))
Eq(F_89(x), F_21(x)*F_25(x)**2)
Eq(F_90(x, k_0), F_21(x)*F_91(x, k_0))
Eq(F_91(x, k_0), (k_0*F_6(x, k_0) - F_6(x, 1))/(k_0 - 1))
Eq(F_92(x, k_0), F_15(x, k_0)*F_6(x, k_0))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_21(x)*F_95(x))
Eq(F_95(x), F_89(x) + F_96(x))
Eq(F_96(x), F_97(x) + F_98(x))
Eq(F_97(x), F_1(x) + F_17(x))
Eq(F_98(x), F_45(x) + F_61(x))
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": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "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, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "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, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [3, 0]]}, {"patt": 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