01234_01243_01324_01342_01423_01432_02314_02413_10234_10243_10324_10342_10423_10432_12304_12403_20134_20143_20314_20341_20413_20431_21304_21403_30124_30142_30214_30241_30412_30421_31204_31402_40123_40132_40213_40231_40312_40321_41203_41302
Counting sequence:
1, 1, 2, 6, 24, 80, 240, 700, 2016, 5724, 16040, 44484, 122352, 334204, 907480, 2451540, 6593344, 17663340, 47155752, 125502980, 333095440, 881853084, 2329366776, 6140182580, 16154850528, 42429700300, 111260640712, 291319949412, 761732957104, 1989211520764, 5188507821720, 13518271607956, 35184202016384, 91485005869356, 237658389920616, 616851366247620, 1599754131742032, 4145631703752540, 10735217369990200, 27779863414956276, 71839573202331680, 185663213068306828, 479545200602038536, 1237904002467160356, 3193812682671752944, 8235832996455968700, 21227121345582100952, 54685146755381574996, 140815679277598718400, 362446666883155333612, 932515990487900985000, 2398251432580693800324, 6165469209491080036496, 15844440658272654684188, 40703621917691420471160, 104529828635540778256820, 268351377562455344241504, 688698141209008065792588, 1766933894855935561514056, 4531923528957582314568164, 11620372900376735676713520, 29787695290120163543343228, 76337337800872008661024024, 195579856570387831925949972, 500958558899122641098951936, 1282842787238907109594690220, 3284295828776555861160473064, 8406425897059795104114716228, 21512146763059710546297463760, 55037941626094736750433812700, 140782730991638777600365451960, 360037674147856553372382130804, 920577483665767768083999329952, 2353363238437414572215855352588, 6015006179425509912373688334216, 15371062010581980744623073972900, 39273034276522901789567787093360, 100325155750115902431014554734908, 256242978177237470143087111915608, 654368997048627246984574955130580, 1670797680932118186617955396591680, 4265374308964355283639468878599020, 10887401412505667317557043896847656, 27786044603050676403583893699061508, 70903255367926244940910258440849168, 180902291483822105446557476201484700, 461489523916597963346585023755716088, 1177120440512097423277383263443983156, 3002082161185527526207492730014859744, 7655404823911519634952361208915626956, 19519060823984123191718352374161339080, 49761796789227360827797620279438699364, 126847158055616824747197762487476064432, 323306261602342745146623778722427634172, 823943200281479598318228965233080308632, 2099574448416880232707604317493148653460, 5349548874607543738354973169426937262976, 13628746514380034210343057492103187592236, 34717505147144821475857898566059551467624, 88429237570821566017004882236931419791300, 225215843534615687936073879904647222930000
Generating function in Maple syntax:
(4*x^6-10*x^5+14*x^4-9*x^3+9*x^2-5*x+1)/(2*x^3-2*x^2+3*x-1)^2
Generating function in latex syntax:
\frac{4 x^{6}-10 x^{5}+14 x^{4}-9 x^{3}+9 x^{2}-5 x +1}{\left(2 x^{3}-2 x^{2}+3 x -1\right)^{2}}
Generating function in sympy syntax:
(4*x**6 - 10*x**5 + 14*x**4 - 9*x**3 + 9*x**2 - 5*x + 1)/(2*x**3 - 2*x**2 + 3*x - 1)**2
Implicit equation for the generating function in Maple syntax:
(2*x^3-2*x^2+3*x-1)^2*F(x)-4*x^6+10*x^5-14*x^4+9*x^3-9*x^2+5*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x^{3}-2 x^{2}+3 x -1\right)^{2} F \! \left(x \right)-4 x^{6}+10 x^{5}-14 x^{4}+9 x^{3}-9 x^{2}+5 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,-11/2548*((((182/33*I*2^(1/3)-7/132*2^(5/6)*13^(1/2))*3^(1/2)-7/44*I*2^(5/6)*13^(1/2)+182/33*2^(1/3))*(4+3*13^(1/2)*2^(1/2)*3^(1/2))^(1/3)-1274/33+((-13/132*I*2^(2/3)-1/3*13^(1/2)*2^(1/6))*3^(1/2)+I*13^(1/2)*2^(1/6)+13/132*2^(2/3))*(4+3*13^(1/2)*2^(1/2)*3^(1/2))^(2/3))*(1/588*(-49*I*3^(1/2)-49)*(8+6*13^(1/2)*2^(1/2)*3^(1/2))^(1/3)+1/3+1/588*(-9*2^(1/6)*(I-1/3*3^(1/2))*13^(1/2)+(2*I*3^(1/2)-2)*2^(2/3))*(4+3*13^(1/2)*2^(1/2)*3^(1/2))^(2/3))^(-n)+(((-182/33*I*2^(1/3)-7/132*2^(5/6)*13^(1/2))*3^(1/2)+7/44*I*2^(5/6)*13^(1/2)+182/33*2^(1/3))*(4+3*13^(1/2)*2^(1/2)*3^(1/2))^(1/3)-1274/33+((13/132*I*2^(2/3)-1/3*13^(1/2)*2^(1/6))*3^(1/2)-I*13^(1/2)*2^(1/6)+13/132*2^(2/3))*(4+3*13^(1/2)*2^(1/2)*3^(1/2))^(2/3))*(1/588*(49*I*3^(1/2)-49)*(8+6*13^(1/2)*2^(1/2)*3^(1/2))^(1/3)+1/3+1/588*(9*2^(1/6)*(I+1/3*3^(1/2))*13^(1/2)+(-2*I*3^(1/2)-2)*2^(2/3))*(4+3*13^(1/2)*2^(1/2)*3^(1/2))^(2/3))^(-n)+2/3*((7/44*2^(5/6)*13^(1/2)*3^(1/2)-182/11*2^(1/3))*(4+3*13^(1/2)*2^(1/2)*3^(1/2))^(1/3)-637/11+(2^(1/6)*3^(1/2)*13^(1/2)-13/44*2^(2/3))*(4+3*13^(1/2)*2^(1/2)*3^(1/2))^(2/3))*(1/294*(-3*2^(1/6)*3^(1/2)*13^(1/2)+2*2^(2/3))*(4+3*13^(1/2)*2^(1/2)*3^(1/2))^(2/3)+1/6*(8+6*13^(1/2)*2^(1/2)*3^(1/2))^(1/3)+1/3)^(-n))*n)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ -\frac{11 \left(\left(\left(\left(\frac{182 i 2^{\frac{1}{3}}}{33}-\frac{7 \,2^{\frac{5}{6}} \sqrt{13}}{132}\right) \sqrt{3}-\frac{7 i 2^{\frac{5}{6}} \sqrt{13}}{44}+\frac{182 \,2^{\frac{1}{3}}}{33}\right) \left(4+3 \sqrt{13}\, \sqrt{2}\, \sqrt{3}\right)^{\frac{1}{3}}-\frac{1274}{33}+\left(\left(-\frac{13 i 2^{\frac{2}{3}}}{132}-\frac{\sqrt{13}\, 2^{\frac{1}{6}}}{3}\right) \sqrt{3}+i \sqrt{13}\, 2^{\frac{1}{6}}+\frac{13 \,2^{\frac{2}{3}}}{132}\right) \left(4+3 \sqrt{13}\, \sqrt{2}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(\frac{\left(-49 i \sqrt{3}-49\right) \left(8+6 \sqrt{13}\, \sqrt{2}\, \sqrt{3}\right)^{\frac{1}{3}}}{588}+\frac{1}{3}+\frac{\left(-9 \,2^{\frac{1}{6}} \left(i-\frac{\sqrt{3}}{3}\right) \sqrt{13}+\left(2 i \sqrt{3}-2\right) 2^{\frac{2}{3}}\right) \left(4+3 \sqrt{13}\, \sqrt{2}\, \sqrt{3}\right)^{\frac{2}{3}}}{588}\right)^{-n}+\left(\left(\left(-\frac{182 i 2^{\frac{1}{3}}}{33}-\frac{7 \,2^{\frac{5}{6}} \sqrt{13}}{132}\right) \sqrt{3}+\frac{7 i 2^{\frac{5}{6}} \sqrt{13}}{44}+\frac{182 \,2^{\frac{1}{3}}}{33}\right) \left(4+3 \sqrt{13}\, \sqrt{2}\, \sqrt{3}\right)^{\frac{1}{3}}-\frac{1274}{33}+\left(\left(\frac{13 i 2^{\frac{2}{3}}}{132}-\frac{\sqrt{13}\, 2^{\frac{1}{6}}}{3}\right) \sqrt{3}-i \sqrt{13}\, 2^{\frac{1}{6}}+\frac{13 \,2^{\frac{2}{3}}}{132}\right) \left(4+3 \sqrt{13}\, \sqrt{2}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(\frac{\left(49 i \sqrt{3}-49\right) \left(8+6 \sqrt{13}\, \sqrt{2}\, \sqrt{3}\right)^{\frac{1}{3}}}{588}+\frac{1}{3}+\frac{\left(9 \,2^{\frac{1}{6}} \left(i+\frac{\sqrt{3}}{3}\right) \sqrt{13}+\left(-2 i \sqrt{3}-2\right) 2^{\frac{2}{3}}\right) \left(4+3 \sqrt{13}\, \sqrt{2}\, \sqrt{3}\right)^{\frac{2}{3}}}{588}\right)^{-n}+\frac{2 \left(\left(\frac{7 \,2^{\frac{5}{6}} \sqrt{13}\, \sqrt{3}}{44}-\frac{182 \,2^{\frac{1}{3}}}{11}\right) \left(4+3 \sqrt{13}\, \sqrt{2}\, \sqrt{3}\right)^{\frac{1}{3}}-\frac{637}{11}+\left(2^{\frac{1}{6}} \sqrt{3}\, \sqrt{13}-\frac{13 \,2^{\frac{2}{3}}}{44}\right) \left(4+3 \sqrt{13}\, \sqrt{2}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(\frac{\left(-3 \,2^{\frac{1}{6}} \sqrt{3}\, \sqrt{13}+2 \,2^{\frac{2}{3}}\right) \left(4+3 \sqrt{13}\, \sqrt{2}\, \sqrt{3}\right)^{\frac{2}{3}}}{294}+\frac{\left(8+6 \sqrt{13}\, \sqrt{2}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}+\frac{1}{3}\right)^{-n}}{3}\right) n}{2548} & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 80
a(6) = 240
a(n+6) = -4*a(n)+8*a(n+1)-16*a(n+2)+16*a(n+3)-13*a(n+4)+6*a(n+5), n >= 7
Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 80
a(6) = 240
a{\left(n + 6 \right)} = - 4 a{\left(n \right)} + 8 a{\left(n + 1 \right)} - 16 a{\left(n + 2 \right)} + 16 a{\left(n + 3 \right)} - 13 a{\left(n + 4 \right)} + 6 a{\left(n + 5 \right)}, \quad n \geq 7
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/25417/
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[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[43,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[16,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[4,x]
F[13,x] = F[14,x]+F[15,x]
F[14,x] = F[1,x]+F[4,x]
F[15,x] = F[4,x]
F[16,x] = F[17,x]+F[7,x]
F[17,x] = F[18,x]+F[19,x]+F[40,x]
F[18,x] = 0
F[19,x] = F[20,x]*F[4,x]
F[20,x] = F[21,x]+F[27,x]
F[21,x] = F[11,x]+F[22,x]
F[22,x] = F[18,x]+F[23,x]+F[25,x]
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[4,x]
F[25,x] = F[26,x]*F[4,x]
F[26,x] = F[15,x]
F[27,x] = F[17,x]+F[28,x]
F[28,x] = F[18,x]+F[29,x]+F[33,x]+F[37,x]
F[29,x] = F[30,x]*F[4,x]
F[30,x] = F[31,x]+F[32,x]
F[31,x] = F[22,x]
F[32,x] = F[28,x]
F[33,x] = F[34,x]*F[4,x]
F[34,x] = F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[4,x]*F[7,x]
F[37,x] = F[38,x]*F[4,x]
F[38,x] = F[39,x]
F[39,x] = F[35,x]
F[40,x] = F[4,x]*F[41,x]
F[41,x] = F[39,x]+F[42,x]
F[42,x] = F[35,x]+F[7,x]
F[43,x] = F[44,x]+F[7,x]
F[44,x] = F[18,x]+F[19,x]+F[45,x]
F[45,x] = F[4,x]*F[46,x]
F[46,x] = F[16,x]+F[47,x]
F[47,x] = F[44,x]+F[48,x]
F[48,x] = F[18,x]+F[29,x]+F[49,x]+F[64,x]
F[49,x] = F[4,x]*F[50,x]
F[50,x] = F[27,x]+F[51,x]
F[51,x] = F[48,x]+F[52,x]
F[52,x] = F[18,x]+F[53,x]+F[54,x]+F[57,x]+F[61,x]
F[53,x] = 0
F[54,x] = F[4,x]*F[55,x]
F[55,x] = F[32,x]+F[56,x]
F[56,x] = F[52,x]
F[57,x] = F[4,x]*F[58,x]
F[58,x] = F[59,x]
F[59,x] = F[60,x]
F[60,x] = F[4,x]*F[44,x]
F[61,x] = F[4,x]*F[62,x]
F[62,x] = F[63,x]
F[63,x] = F[59,x]
F[64,x] = F[4,x]*F[65,x]
F[65,x] = F[63,x]+F[66,x]
F[66,x] = F[44,x]+F[59,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_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{43}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{16}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{15}\! \left(x \right)
F_{14}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{15}\! \left(x \right) = F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{7}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)+F_{40}\! \left(x \right)
F_{18}\! \left(x \right) = 0
F_{19}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{27}\! \left(x \right)
F_{21}\! \left(x \right) = F_{11}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{18}\! \left(x \right)+F_{23}\! \left(x \right)+F_{25}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{15}\! \left(x \right)
F_{27}\! \left(x \right) = F_{17}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{18}\! \left(x \right)+F_{29}\! \left(x \right)+F_{33}\! \left(x \right)+F_{37}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{32}\! \left(x \right)
F_{31}\! \left(x \right) = F_{22}\! \left(x \right)
F_{32}\! \left(x \right) = F_{28}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{4}\! \left(x \right) F_{7}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{35}\! \left(x \right)
F_{40}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{39}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{35}\! \left(x \right)+F_{7}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{7}\! \left(x \right)
F_{44}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{16}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{44}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{18}\! \left(x \right)+F_{29}\! \left(x \right)+F_{49}\! \left(x \right)+F_{64}\! \left(x \right)
F_{49}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{27}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{48}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{18}\! \left(x \right)+F_{53}\! \left(x \right)+F_{54}\! \left(x \right)+F_{57}\! \left(x \right)+F_{61}\! \left(x \right)
F_{53}\! \left(x \right) = 0
F_{54}\! \left(x \right) = F_{4}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{32}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{52}\! \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_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right)
F_{61}\! \left(x \right) = F_{4}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{59}\! \left(x \right)
F_{64}\! \left(x \right) = F_{4}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{63}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{44}\! \left(x \right)+F_{59}\! \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_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_43(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_16(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_4(x))
Eq(F_13(x), F_14(x) + F_15(x))
Eq(F_14(x), F_1(x) + F_4(x))
Eq(F_15(x), F_4(x))
Eq(F_16(x), F_17(x) + F_7(x))
Eq(F_17(x), F_18(x) + F_19(x) + F_40(x))
Eq(F_18(x), 0)
Eq(F_19(x), F_20(x)*F_4(x))
Eq(F_20(x), F_21(x) + F_27(x))
Eq(F_21(x), F_11(x) + F_22(x))
Eq(F_22(x), F_18(x) + F_23(x) + F_25(x))
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_4(x))
Eq(F_25(x), F_26(x)*F_4(x))
Eq(F_26(x), F_15(x))
Eq(F_27(x), F_17(x) + F_28(x))
Eq(F_28(x), F_18(x) + F_29(x) + F_33(x) + F_37(x))
Eq(F_29(x), F_30(x)*F_4(x))
Eq(F_30(x), F_31(x) + F_32(x))
Eq(F_31(x), F_22(x))
Eq(F_32(x), F_28(x))
Eq(F_33(x), F_34(x)*F_4(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_4(x)*F_7(x))
Eq(F_37(x), F_38(x)*F_4(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_35(x))
Eq(F_40(x), F_4(x)*F_41(x))
Eq(F_41(x), F_39(x) + F_42(x))
Eq(F_42(x), F_35(x) + F_7(x))
Eq(F_43(x), F_44(x) + F_7(x))
Eq(F_44(x), F_18(x) + F_19(x) + F_45(x))
Eq(F_45(x), F_4(x)*F_46(x))
Eq(F_46(x), F_16(x) + F_47(x))
Eq(F_47(x), F_44(x) + F_48(x))
Eq(F_48(x), F_18(x) + F_29(x) + F_49(x) + F_64(x))
Eq(F_49(x), F_4(x)*F_50(x))
Eq(F_50(x), F_27(x) + F_51(x))
Eq(F_51(x), F_48(x) + F_52(x))
Eq(F_52(x), F_18(x) + F_53(x) + F_54(x) + F_57(x) + F_61(x))
Eq(F_53(x), 0)
Eq(F_54(x), F_4(x)*F_55(x))
Eq(F_55(x), F_32(x) + F_56(x))
Eq(F_56(x), F_52(x))
Eq(F_57(x), F_4(x)*F_58(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_4(x)*F_44(x))
Eq(F_61(x), F_4(x)*F_62(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_59(x))
Eq(F_64(x), F_4(x)*F_65(x))
Eq(F_65(x), F_63(x) + F_66(x))
Eq(F_66(x), F_44(x) + F_59(x))
Pack JSON:
{"name": "point_placements", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"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, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 0, 3], "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, 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"pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"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, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3, 4], "pos": [[0, 0], [0, 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