0132_0231_1230_2310
Counting sequence:
1, 1, 2, 6, 20, 66, 208, 624, 1792, 4960, 13312, 34816, 89088, 223744, 552960, 1347584, 3244032, 7725056, 18219008, 42598400, 98828288, 227672064, 521142272, 1185939456, 2684354560, 6046089216, 13555990528, 30266097664, 67310190592, 149149450240, 329370304512, 725044166656, 1591285383168, 3482681606144, 7602092113920, 16552803958784, 35957466202112, 77936476553216, 168568876433408, 363869629317120, 783951790604288, 1685963642241024, 3619592278638592, 7758154045587456, 16602625579417600, 35476842181820416, 75699176549122048, 161302753841250304, 343258734098644992, 729547955261931520, 1548675321862029312, 3283687078306512896, 6954683724566888448, 14713822932572831744, 31097355426993274880, 65657978967434461184, 138494695740897492992, 291860277451372363776, 614507161955449438208, 1292713237040427171840, 2717147755982186610688, 5706529102239664963584, 11975395668351319539712, 25111783291841733984256, 52619337470256495984640, 110180096509257938108416, 230547407433221976096768, 482087209622325421932544, 1007413587353426032852992, 2103851161606574361804800, 4390915385353231990259712, 9158734645620497539137536, 19092527690241975598972928, 39778263772642097751916544, 82830308109533577048227840, 172385266090673528880758784, 358578731777257900366364672, 745501107184699411305332736, 1549162879972421373062545408, 3217631626768061462803906560, 6679919616280633504838975488, 13861392331973886288534175744, 28750673842075111032862277632, 59607296461918906088062713856, 123528040248222809071477063680, 255888492534550098893357449216, 529857679627256591723620466688, 1096718160741277753226647568384, 2269144092010102043890094702592, 4693146745809559626543351726080, 9702974027918810594659335667712, 20053390696383875073090913304576, 41430139294763821660048990404608, 85564558605346556530615117676544, 176654043606023765228105026764800, 364593148610173057042190469955584, 752231788991682753281903036465152, 1551515202996524240052171986436096, 3199074746000965423352117626667008, 6594159966062220817910662986465280, 13588263696496448011993535834226688
Generating function in Maple syntax:
(x-1)*(2*x^4+6*x^3-12*x^2+6*x-1)/(2*x-1)^4
Generating function in latex syntax:
\frac{\left(x -1\right) \left(2 x^{4}+6 x^{3}-12 x^{2}+6 x -1\right)}{\left(2 x -1\right)^{4}}
Generating function in sympy syntax:
(x - 1)*(2*x**4 + 6*x**3 - 12*x**2 + 6*x - 1)/(2*x - 1)**4
Implicit equation for the generating function in Maple syntax:
-(2*x-1)^4*F(x)+(x-1)*(2*x^4+6*x^3-12*x^2+6*x-1) = 0
Implicit equation for the generating function in latex syntax:
-\left(2 x -1\right)^{4} F \! \left(x \right)+\left(x -1\right) \left(2 x^{4}+6 x^{3}-12 x^{2}+6 x -1\right) = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,1/96*2^n*(n+6)*(n^2-3*n+8))
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ \frac{2^{n} \left(n +6\right) \left(n^{2}-3 n +8\right)}{96} & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 66
a(n+4) = -16*a(n)+32*a(n+1)-24*a(n+2)+8*a(n+3), n >= 6
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) = 20
a \! \left(5\right) = 66
a \! \left(n +4\right) = -16 a \! \left(n \right)+32 a \! \left(n +1\right)-24 a \! \left(n +2\right)+8 a \! \left(n +3\right), \quad n \geq 6
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15353/
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[3,x] = F[12,x]*F[4,x]
F[4,x] = F[22,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[12,x]*F[8,x]
F[8,x] = F[13,x]+F[9,x]
F[9,x] = F[1,x]+F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[9,x]
F[12,x] = x
F[13,x] = F[14,x]+F[17,x]
F[14,x] = F[15,x]
F[15,x] = F[12,x]*F[16,x]
F[16,x] = F[1,x]+F[14,x]
F[17,x] = F[18,x]+F[19,x]+F[21,x]
F[18,x] = 0
F[19,x] = F[12,x]*F[20,x]
F[20,x] = F[10,x]+F[17,x]
F[21,x] = F[12,x]*F[13,x]
F[22,x] = F[23,x]+F[33,x]
F[23,x] = F[24,x]
F[24,x] = F[12,x]*F[25,x]
F[25,x] = F[16,x]+F[26,x]
F[26,x] = F[14,x]+F[27,x]
F[27,x] = F[18,x]+F[28,x]+F[30,x]
F[28,x] = F[12,x]*F[29,x]
F[29,x] = F[14,x]+F[27,x]
F[30,x] = F[12,x]*F[31,x]
F[31,x] = F[14,x]+F[32,x]
F[32,x] = F[30,x]
F[33,x] = F[18,x]+F[34,x]+F[77,x]
F[34,x] = F[12,x]*F[35,x]
F[35,x] = F[36,x]+F[45,x]
F[36,x] = F[37,x]+F[6,x]
F[37,x] = F[18,x]+F[19,x]+F[38,x]
F[38,x] = F[12,x]*F[39,x]
F[39,x] = F[13,x]+F[40,x]
F[40,x] = F[32,x]+F[41,x]
F[41,x] = 2*F[18,x]+F[42,x]+F[44,x]
F[42,x] = F[12,x]*F[43,x]
F[43,x] = F[17,x]+F[41,x]
F[44,x] = F[12,x]*F[40,x]
F[45,x] = F[46,x]+F[56,x]
F[46,x] = F[18,x]+F[47,x]+F[49,x]
F[47,x] = F[12,x]*F[48,x]
F[48,x] = F[46,x]+F[6,x]
F[49,x] = F[12,x]*F[50,x]
F[50,x] = F[13,x]+F[51,x]
F[51,x] = F[27,x]+F[52,x]
F[52,x] = F[18,x]+F[42,x]+F[53,x]+F[55,x]
F[53,x] = F[12,x]*F[54,x]
F[54,x] = F[17,x]+F[52,x]
F[55,x] = F[12,x]*F[51,x]
F[56,x] = F[18,x]+F[42,x]+F[57,x]+F[59,x]
F[57,x] = F[12,x]*F[58,x]
F[58,x] = F[37,x]+F[56,x]
F[59,x] = F[12,x]*F[60,x]
F[60,x] = F[51,x]+F[61,x]
F[61,x] = F[62,x]+F[68,x]
F[62,x] = 2*F[18,x]+F[63,x]+F[65,x]
F[63,x] = F[12,x]*F[64,x]
F[64,x] = F[32,x]+F[62,x]
F[65,x] = F[12,x]*F[66,x]
F[66,x] = F[32,x]+F[67,x]
F[67,x] = F[65,x]
F[68,x] = 2*F[18,x]+F[69,x]+F[71,x]+F[76,x]
F[69,x] = F[12,x]*F[70,x]
F[70,x] = F[41,x]+F[68,x]
F[71,x] = F[12,x]*F[72,x]
F[72,x] = F[41,x]+F[73,x]
F[73,x] = 3*F[18,x]+F[71,x]+F[74,x]
F[74,x] = F[12,x]*F[75,x]
F[75,x] = F[67,x]+F[73,x]
F[76,x] = F[12,x]*F[61,x]
F[77,x] = F[12,x]*F[78,x]
F[78,x] = F[79,x]+F[85,x]
F[79,x] = F[23,x]+F[80,x]
F[80,x] = F[18,x]+F[81,x]+F[84,x]
F[81,x] = F[12,x]*F[82,x]
F[82,x] = F[20,x]+F[83,x]
F[83,x] = F[17,x]+F[52,x]
F[84,x] = F[12,x]*F[79,x]
F[85,x] = F[86,x]+F[91,x]
F[86,x] = F[18,x]+F[30,x]+F[87,x]
F[87,x] = F[12,x]*F[88,x]
F[88,x] = F[89,x]+F[90,x]
F[89,x] = F[14,x]+F[32,x]
F[90,x] = F[27,x]+F[62,x]
F[91,x] = F[18,x]+F[42,x]+F[92,x]+F[96,x]
F[92,x] = F[12,x]*F[93,x]
F[93,x] = F[94,x]+F[95,x]
F[94,x] = F[17,x]+F[41,x]
F[95,x] = F[52,x]+F[68,x]
F[96,x] = F[12,x]*F[85,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_{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_{22}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{13}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{9}\! \left(x \right)
F_{12}\! \left(x \right) = x
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{17}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{12}\! \left(x \right) F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)+F_{21}\! \left(x \right)
F_{18}\! \left(x \right) = 0
F_{19}\! \left(x \right) = F_{12}\! \left(x \right) F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{10}\! \left(x \right)+F_{17}\! \left(x \right)
F_{21}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{33}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{12}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{16}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{14}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{18}\! \left(x \right)+F_{28}\! \left(x \right)+F_{30}\! \left(x \right)
F_{28}\! \left(x \right) = F_{12}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{14}\! \left(x \right)+F_{27}\! \left(x \right)
F_{30}\! \left(x \right) = F_{12}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{14}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{30}\! \left(x \right)
F_{33}\! \left(x \right) = F_{18}\! \left(x \right)+F_{34}\! \left(x \right)+F_{77}\! \left(x \right)
F_{34}\! \left(x \right) = F_{12}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{45}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{6}\! \left(x \right)
F_{37}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{12}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{13}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{32}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{42}\! \left(x \right)+F_{44}\! \left(x \right)
F_{42}\! \left(x \right) = F_{12}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{17}\! \left(x \right)+F_{41}\! \left(x \right)
F_{44}\! \left(x \right) = F_{12}\! \left(x \right) F_{40}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{56}\! \left(x \right)
F_{46}\! \left(x \right) = F_{18}\! \left(x \right)+F_{47}\! \left(x \right)+F_{49}\! \left(x \right)
F_{47}\! \left(x \right) = F_{12}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{46}\! \left(x \right)+F_{6}\! \left(x \right)
F_{49}\! \left(x \right) = F_{12}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{13}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{27}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{18}\! \left(x \right)+F_{42}\! \left(x \right)+F_{53}\! \left(x \right)+F_{55}\! \left(x \right)
F_{53}\! \left(x \right) = F_{12}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{17}\! \left(x \right)+F_{52}\! \left(x \right)
F_{55}\! \left(x \right) = F_{12}\! \left(x \right) F_{51}\! \left(x \right)
F_{56}\! \left(x \right) = F_{18}\! \left(x \right)+F_{42}\! \left(x \right)+F_{57}\! \left(x \right)+F_{59}\! \left(x \right)
F_{57}\! \left(x \right) = F_{12}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{37}\! \left(x \right)+F_{56}\! \left(x \right)
F_{59}\! \left(x \right) = F_{12}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{51}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{68}\! \left(x \right)
F_{62}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{63}\! \left(x \right)+F_{65}\! \left(x \right)
F_{63}\! \left(x \right) = F_{12}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{32}\! \left(x \right)+F_{62}\! \left(x \right)
F_{65}\! \left(x \right) = F_{12}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{32}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{65}\! \left(x \right)
F_{68}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{69}\! \left(x \right)+F_{71}\! \left(x \right)+F_{76}\! \left(x \right)
F_{69}\! \left(x \right) = F_{12}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{41}\! \left(x \right)+F_{68}\! \left(x \right)
F_{71}\! \left(x \right) = F_{12}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{41}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = 3 F_{18}\! \left(x \right)+F_{71}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{12}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{67}\! \left(x \right)+F_{73}\! \left(x \right)
F_{76}\! \left(x \right) = F_{12}\! \left(x \right) F_{61}\! \left(x \right)
F_{77}\! \left(x \right) = F_{12}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{85}\! \left(x \right)
F_{79}\! \left(x \right) = F_{23}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{18}\! \left(x \right)+F_{81}\! \left(x \right)+F_{84}\! \left(x \right)
F_{81}\! \left(x \right) = F_{12}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{20}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{17}\! \left(x \right)+F_{52}\! \left(x \right)
F_{84}\! \left(x \right) = F_{12}\! \left(x \right) F_{79}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{91}\! \left(x \right)
F_{86}\! \left(x \right) = F_{18}\! \left(x \right)+F_{30}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{12}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)+F_{90}\! \left(x \right)
F_{89}\! \left(x \right) = F_{14}\! \left(x \right)+F_{32}\! \left(x \right)
F_{90}\! \left(x \right) = F_{27}\! \left(x \right)+F_{62}\! \left(x \right)
F_{91}\! \left(x \right) = F_{18}\! \left(x \right)+F_{42}\! \left(x \right)+F_{92}\! \left(x \right)+F_{96}\! \left(x \right)
F_{92}\! \left(x \right) = F_{12}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)+F_{95}\! \left(x \right)
F_{94}\! \left(x \right) = F_{17}\! \left(x \right)+F_{41}\! \left(x \right)
F_{95}\! \left(x \right) = F_{52}\! \left(x \right)+F_{68}\! \left(x \right)
F_{96}\! \left(x \right) = F_{12}\! \left(x \right) F_{85}\! \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_3(x))
Eq(F_3(x), F_12(x)*F_4(x))
Eq(F_4(x), F_22(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_12(x)*F_8(x))
Eq(F_8(x), F_13(x) + F_9(x))
Eq(F_9(x), F_1(x) + F_10(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_9(x))
Eq(F_12(x), x)
Eq(F_13(x), F_14(x) + F_17(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_12(x)*F_16(x))
Eq(F_16(x), F_1(x) + F_14(x))
Eq(F_17(x), F_18(x) + F_19(x) + F_21(x))
Eq(F_18(x), 0)
Eq(F_19(x), F_12(x)*F_20(x))
Eq(F_20(x), F_10(x) + F_17(x))
Eq(F_21(x), F_12(x)*F_13(x))
Eq(F_22(x), F_23(x) + F_33(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_12(x)*F_25(x))
Eq(F_25(x), F_16(x) + F_26(x))
Eq(F_26(x), F_14(x) + F_27(x))
Eq(F_27(x), F_18(x) + F_28(x) + F_30(x))
Eq(F_28(x), F_12(x)*F_29(x))
Eq(F_29(x), F_14(x) + F_27(x))
Eq(F_30(x), F_12(x)*F_31(x))
Eq(F_31(x), F_14(x) + F_32(x))
Eq(F_32(x), F_30(x))
Eq(F_33(x), F_18(x) + F_34(x) + F_77(x))
Eq(F_34(x), F_12(x)*F_35(x))
Eq(F_35(x), F_36(x) + F_45(x))
Eq(F_36(x), F_37(x) + F_6(x))
Eq(F_37(x), F_18(x) + F_19(x) + F_38(x))
Eq(F_38(x), F_12(x)*F_39(x))
Eq(F_39(x), F_13(x) + F_40(x))
Eq(F_40(x), F_32(x) + F_41(x))
Eq(F_41(x), 2*F_18(x) + F_42(x) + F_44(x))
Eq(F_42(x), F_12(x)*F_43(x))
Eq(F_43(x), F_17(x) + F_41(x))
Eq(F_44(x), F_12(x)*F_40(x))
Eq(F_45(x), F_46(x) + F_56(x))
Eq(F_46(x), F_18(x) + F_47(x) + F_49(x))
Eq(F_47(x), F_12(x)*F_48(x))
Eq(F_48(x), F_46(x) + F_6(x))
Eq(F_49(x), F_12(x)*F_50(x))
Eq(F_50(x), F_13(x) + F_51(x))
Eq(F_51(x), F_27(x) + F_52(x))
Eq(F_52(x), F_18(x) + F_42(x) + F_53(x) + F_55(x))
Eq(F_53(x), F_12(x)*F_54(x))
Eq(F_54(x), F_17(x) + F_52(x))
Eq(F_55(x), F_12(x)*F_51(x))
Eq(F_56(x), F_18(x) + F_42(x) + F_57(x) + F_59(x))
Eq(F_57(x), F_12(x)*F_58(x))
Eq(F_58(x), F_37(x) + F_56(x))
Eq(F_59(x), F_12(x)*F_60(x))
Eq(F_60(x), F_51(x) + F_61(x))
Eq(F_61(x), F_62(x) + F_68(x))
Eq(F_62(x), 2*F_18(x) + F_63(x) + F_65(x))
Eq(F_63(x), F_12(x)*F_64(x))
Eq(F_64(x), F_32(x) + F_62(x))
Eq(F_65(x), F_12(x)*F_66(x))
Eq(F_66(x), F_32(x) + F_67(x))
Eq(F_67(x), F_65(x))
Eq(F_68(x), 2*F_18(x) + F_69(x) + F_71(x) + F_76(x))
Eq(F_69(x), F_12(x)*F_70(x))
Eq(F_70(x), F_41(x) + F_68(x))
Eq(F_71(x), F_12(x)*F_72(x))
Eq(F_72(x), F_41(x) + F_73(x))
Eq(F_73(x), 3*F_18(x) + F_71(x) + F_74(x))
Eq(F_74(x), F_12(x)*F_75(x))
Eq(F_75(x), F_67(x) + F_73(x))
Eq(F_76(x), F_12(x)*F_61(x))
Eq(F_77(x), F_12(x)*F_78(x))
Eq(F_78(x), F_79(x) + F_85(x))
Eq(F_79(x), F_23(x) + F_80(x))
Eq(F_80(x), F_18(x) + F_81(x) + F_84(x))
Eq(F_81(x), F_12(x)*F_82(x))
Eq(F_82(x), F_20(x) + F_83(x))
Eq(F_83(x), F_17(x) + F_52(x))
Eq(F_84(x), F_12(x)*F_79(x))
Eq(F_85(x), F_86(x) + F_91(x))
Eq(F_86(x), F_18(x) + F_30(x) + F_87(x))
Eq(F_87(x), F_12(x)*F_88(x))
Eq(F_88(x), F_89(x) + F_90(x))
Eq(F_89(x), F_14(x) + F_32(x))
Eq(F_90(x), F_27(x) + F_62(x))
Eq(F_91(x), F_18(x) + F_42(x) + F_92(x) + F_96(x))
Eq(F_92(x), F_12(x)*F_93(x))
Eq(F_93(x), F_94(x) + F_95(x))
Eq(F_94(x), F_17(x) + F_41(x))
Eq(F_95(x), F_52(x) + F_68(x))
Eq(F_96(x), F_12(x)*F_85(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "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.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_placements", "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:
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{"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 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], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 1], [2, 1], [2, 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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": 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{"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[1, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 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": [], 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