0132_1203_1320_2031_2301
Counting sequence:
1, 1, 2, 6, 19, 55, 146, 363, 860, 1966, 4377, 9556, 20565, 43793, 92540, 194441, 406826, 848464, 1765099, 3664618, 7595579, 15720651, 32496262, 67097431, 138398504, 285196770, 587183981, 1207937968, 2483003025, 5100244981, 10468949952, 21474799061, 44023372310, 90194265188, 184683539615, 377957061286, 773094045271, 1580547889039, 3229815322154, 6597069672963, 13469017336564, 27487790579926, 56075092890497, 114349209150156, 233096464936589, 474989023032985, 967570232261316, 1970324836776673, 4011018417911490, 8162774324375096, 16607023625675027, 33776997205004066, 68679894317103155, 139611588448164883, 283726776523995790, 576460752303051631, 1170935903115929216, 2377900603251192714, 4827858800540711509, 9799832789157706408, 19887895954467583049, 40352252661239080701, 81857426827085533832, 166020696663385323181, 336653079345198633774, 682529530727252682700, 1383505805528215598151, 2803905099203851024478, 5681597174702541026255, 11510768301994759284311, 23316684509168872263602, 47223664828696451100571, 95627921278110314481100, 193617025797655452602878, 391956418078180551513065, 793357569122100394609476, 1605604604175679371294661, 3248988140214315905587489, 6573534144154546135953164, 13298184015760920920176953, 26898599486425499135539034, 54401661882658312860018976, 110012249584931254896414267, 222442350809091768143996506, 449720404896642052988662059, 909112216350201139376909915, 1837567245814236345551150486, 3713820117856140824695029383, 7505011488167617916573487320, 15164765481245908367511704626, 30639015972313161803750639677, 61897001964269013744953404576, 125031943967823407764808614145, 252539768014217576079418279173, 510031296185576673258435983440, 1029966112685436388716068018821, 2079739265999438861830525217606, 4199092613256009892457825741364, 8477413389026284122509198907119, 17113283103081096920205489336598, 34543478856219251190785158248519
Generating function in Maple syntax:
(3*x^7-10*x^6+28*x^5-48*x^4+48*x^3-27*x^2+8*x-1)/(2*x-1)^2/(x-1)^5
Generating function in latex syntax:
\frac{3 x^{7}-10 x^{6}+28 x^{5}-48 x^{4}+48 x^{3}-27 x^{2}+8 x -1}{\left(2 x -1\right)^{2} \left(x -1\right)^{5}}
Generating function in sympy syntax:
(3*x**7 - 10*x**6 + 28*x**5 - 48*x**4 + 48*x**3 - 27*x**2 + 8*x - 1)/((x - 1)**5*(2*x - 1)**2)
Implicit equation for the generating function in Maple syntax:
(2*x-1)^2*(x-1)^5*F(x)-3*x^7+10*x^6-28*x^5+48*x^4-48*x^3+27*x^2-8*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right)^{2} \left(x -1\right)^{5} F \! \left(x \right)-3 x^{7}+10 x^{6}-28 x^{5}+48 x^{4}-48 x^{3}+27 x^{2}-8 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,-2+1/4*2^n*n+9/4*2^n-1/24*n^4+1/12*n^3-35/24*n^2-7/12*n)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ -2+\frac{2^{n} n}{4}+\frac{9 \,2^{n}}{4}-\frac{n^{4}}{24}+\frac{n^{3}}{12}-\frac{35 n^{2}}{24}-\frac{7 n}{12} & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 55
a(6) = 146
a(7) = 363
a(n+2) = -1/24*n^4+5/12*n^3-47/24*n^2-4*a(n)+4*a(n+1)+55/12*n-1, n >= 8
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) = 55
a \! \left(6\right) = 146
a \! \left(7\right) = 363
a \! \left(n +2\right) = -\frac{n^{4}}{24}+\frac{5 n^{3}}{12}-\frac{47 n^{2}}{24}-4 a \! \left(n \right)+4 a \! \left(n +1\right)+\frac{55 n}{12}-1, \quad n \geq 8
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/19936/
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[28,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[6,x]
F[14,x] = F[15,x]+F[16,x]+F[20,x]
F[15,x] = 0
F[16,x] = F[12,x]*F[17,x]
F[17,x] = F[18,x]+F[19,x]
F[18,x] = F[10,x]
F[19,x] = F[14,x]
F[20,x] = F[12,x]*F[21,x]
F[21,x] = F[22,x]+F[25,x]
F[22,x] = F[23,x]
F[23,x] = F[12,x]*F[24,x]
F[24,x] = F[1,x]+F[22,x]
F[25,x] = F[15,x]+F[20,x]+F[26,x]
F[26,x] = F[12,x]*F[27,x]
F[27,x] = F[10,x]+F[25,x]
F[28,x] = F[29,x]+F[6,x]
F[29,x] = F[15,x]+F[30,x]+F[98,x]
F[30,x] = F[12,x]*F[31,x]
F[31,x] = F[32,x]+F[54,x]
F[32,x] = F[33,x]+F[6,x]
F[33,x] = F[34,x]
F[34,x] = F[12,x]*F[35,x]
F[35,x] = F[36,x]+F[39,x]
F[36,x] = F[12,x]+F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[12,x]*F[36,x]
F[39,x] = F[40,x]+F[41,x]
F[40,x] = F[34,x]
F[41,x] = 2*F[15,x]+F[42,x]+F[46,x]
F[42,x] = F[12,x]*F[43,x]
F[43,x] = F[44,x]+F[45,x]
F[44,x] = F[37,x]
F[45,x] = F[41,x]
F[46,x] = F[12,x]*F[47,x]
F[47,x] = F[48,x]+F[51,x]
F[48,x] = F[49,x]
F[49,x] = F[12,x]*F[50,x]
F[50,x] = F[12,x]+F[48,x]
F[51,x] = 2*F[15,x]+F[46,x]+F[52,x]
F[52,x] = F[12,x]*F[53,x]
F[53,x] = F[37,x]+F[51,x]
F[54,x] = F[29,x]+F[55,x]
F[55,x] = 2*F[15,x]+F[56,x]+F[60,x]
F[56,x] = F[12,x]*F[57,x]
F[57,x] = F[58,x]+F[59,x]
F[58,x] = F[33,x]
F[59,x] = F[55,x]
F[60,x] = F[12,x]*F[61,x]
F[61,x] = F[62,x]+F[67,x]
F[62,x] = F[63,x]+F[65,x]
F[63,x] = F[64,x]
F[64,x] = F[12,x]*F[22,x]
F[65,x] = F[66,x]
F[66,x] = F[12,x]*F[62,x]
F[67,x] = F[68,x]+F[88,x]
F[68,x] = F[69,x]
F[69,x] = F[12,x]*F[70,x]
F[70,x] = F[71,x]+F[74,x]
F[71,x] = F[63,x]+F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[12,x]*F[71,x]
F[74,x] = F[68,x]+F[75,x]
F[75,x] = 3*F[15,x]+F[76,x]+F[80,x]
F[76,x] = F[12,x]*F[77,x]
F[77,x] = F[78,x]+F[79,x]
F[78,x] = F[72,x]
F[79,x] = F[75,x]
F[80,x] = F[12,x]*F[81,x]
F[81,x] = F[82,x]+F[85,x]
F[82,x] = F[83,x]
F[83,x] = F[12,x]*F[84,x]
F[84,x] = F[63,x]+F[82,x]
F[85,x] = 3*F[15,x]+F[80,x]+F[86,x]
F[86,x] = F[12,x]*F[87,x]
F[87,x] = F[72,x]+F[85,x]
F[88,x] = 3*F[15,x]+F[89,x]+F[93,x]
F[89,x] = F[12,x]*F[90,x]
F[90,x] = F[91,x]+F[92,x]
F[91,x] = F[65,x]
F[92,x] = F[88,x]
F[93,x] = F[12,x]*F[94,x]
F[94,x] = F[82,x]+F[95,x]
F[95,x] = 3*F[15,x]+F[93,x]+F[96,x]
F[96,x] = F[12,x]*F[97,x]
F[97,x] = F[65,x]+F[95,x]
F[98,x] = F[12,x]*F[99,x]
F[99,x] = F[100,x]+F[21,x]
F[100,x] = F[101,x]+F[121,x]
F[101,x] = F[102,x]
F[102,x] = F[103,x]*F[12,x]
F[103,x] = F[104,x]+F[107,x]
F[104,x] = F[105,x]+F[22,x]
F[105,x] = F[106,x]
F[106,x] = F[104,x]*F[12,x]
F[107,x] = F[101,x]+F[108,x]
F[108,x] = 2*F[15,x]+F[109,x]+F[113,x]
F[109,x] = F[110,x]*F[12,x]
F[110,x] = F[111,x]+F[112,x]
F[111,x] = F[105,x]
F[112,x] = F[108,x]
F[113,x] = F[114,x]*F[12,x]
F[114,x] = F[115,x]+F[118,x]
F[115,x] = F[116,x]
F[116,x] = F[117,x]*F[12,x]
F[117,x] = F[115,x]+F[22,x]
F[118,x] = 2*F[15,x]+F[113,x]+F[119,x]
F[119,x] = F[12,x]*F[120,x]
F[120,x] = F[105,x]+F[118,x]
F[121,x] = 2*F[15,x]+F[122,x]+F[126,x]
F[122,x] = F[12,x]*F[123,x]
F[123,x] = F[124,x]+F[125,x]
F[124,x] = F[25,x]
F[125,x] = F[121,x]
F[126,x] = F[12,x]*F[127,x]
F[127,x] = F[115,x]+F[128,x]
F[128,x] = 2*F[15,x]+F[126,x]+F[129,x]
F[129,x] = F[12,x]*F[130,x]
F[130,x] = F[128,x]+F[25,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_{28}\! \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_{6}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{20}\! \left(x \right)
F_{15}\! \left(x \right) = 0
F_{16}\! \left(x \right) = F_{12}\! \left(x \right) F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)
F_{18}\! \left(x \right) = F_{10}\! \left(x \right)
F_{19}\! \left(x \right) = F_{14}\! \left(x \right)
F_{20}\! \left(x \right) = F_{12}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{25}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{12}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{1}\! \left(x \right)+F_{22}\! \left(x \right)
F_{25}\! \left(x \right) = F_{15}\! \left(x \right)+F_{20}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{12}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{10}\! \left(x \right)+F_{25}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{6}\! \left(x \right)
F_{29}\! \left(x \right) = F_{15}\! \left(x \right)+F_{30}\! \left(x \right)+F_{98}\! \left(x \right)
F_{30}\! \left(x \right) = F_{12}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{54}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{6}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \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_{39}\! \left(x \right)
F_{36}\! \left(x \right) = F_{12}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{12}\! \left(x \right) F_{36}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{41}\! \left(x \right)
F_{40}\! \left(x \right) = F_{34}\! \left(x \right)
F_{41}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{42}\! \left(x \right)+F_{46}\! \left(x \right)
F_{42}\! \left(x \right) = F_{12}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{45}\! \left(x \right)
F_{44}\! \left(x \right) = F_{37}\! \left(x \right)
F_{45}\! \left(x \right) = F_{41}\! \left(x \right)
F_{46}\! \left(x \right) = F_{12}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{51}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{12}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{12}\! \left(x \right)+F_{48}\! \left(x \right)
F_{51}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{46}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{12}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{37}\! \left(x \right)+F_{51}\! \left(x \right)
F_{54}\! \left(x \right) = F_{29}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{56}\! \left(x \right)+F_{60}\! \left(x \right)
F_{56}\! \left(x \right) = F_{12}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{59}\! \left(x \right)
F_{58}\! \left(x \right) = F_{33}\! \left(x \right)
F_{59}\! \left(x \right) = F_{55}\! \left(x \right)
F_{60}\! \left(x \right) = F_{12}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{67}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{65}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{12}\! \left(x \right) F_{22}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{12}\! \left(x \right) F_{62}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{88}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{12}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{74}\! \left(x \right)
F_{71}\! \left(x \right) = F_{63}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{12}\! \left(x \right) F_{71}\! \left(x \right)
F_{74}\! \left(x \right) = F_{68}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = 3 F_{15}\! \left(x \right)+F_{76}\! \left(x \right)+F_{80}\! \left(x \right)
F_{76}\! \left(x \right) = F_{12}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{79}\! \left(x \right)
F_{78}\! \left(x \right) = F_{72}\! \left(x \right)
F_{79}\! \left(x \right) = F_{75}\! \left(x \right)
F_{80}\! \left(x \right) = F_{12}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{85}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{12}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{63}\! \left(x \right)+F_{82}\! \left(x \right)
F_{85}\! \left(x \right) = 3 F_{15}\! \left(x \right)+F_{80}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{12}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{72}\! \left(x \right)+F_{85}\! \left(x \right)
F_{88}\! \left(x \right) = 3 F_{15}\! \left(x \right)+F_{89}\! \left(x \right)+F_{93}\! \left(x \right)
F_{89}\! \left(x \right) = F_{12}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)+F_{92}\! \left(x \right)
F_{91}\! \left(x \right) = F_{65}\! \left(x \right)
F_{92}\! \left(x \right) = F_{88}\! \left(x \right)
F_{93}\! \left(x \right) = F_{12}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{82}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = 3 F_{15}\! \left(x \right)+F_{93}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{12}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{65}\! \left(x \right)+F_{95}\! \left(x \right)
F_{98}\! \left(x \right) = F_{12}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{21}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{121}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{12}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{107}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{22}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{104}\! \left(x \right) F_{12}\! \left(x \right)
F_{107}\! \left(x \right) = F_{101}\! \left(x \right)+F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{109}\! \left(x \right)+F_{113}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{12}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{112}\! \left(x \right)
F_{111}\! \left(x \right) = F_{105}\! \left(x \right)
F_{112}\! \left(x \right) = F_{108}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{12}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{118}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{12}\! \left(x \right)
F_{117}\! \left(x \right) = F_{115}\! \left(x \right)+F_{22}\! \left(x \right)
F_{118}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{113}\! \left(x \right)+F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{12}\! \left(x \right) F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{105}\! \left(x \right)+F_{118}\! \left(x \right)
F_{121}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{122}\! \left(x \right)+F_{126}\! \left(x \right)
F_{122}\! \left(x \right) = F_{12}\! \left(x \right) F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{125}\! \left(x \right)
F_{124}\! \left(x \right) = F_{25}\! \left(x \right)
F_{125}\! \left(x \right) = F_{121}\! \left(x \right)
F_{126}\! \left(x \right) = F_{12}\! \left(x \right) F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{115}\! \left(x \right)+F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{126}\! \left(x \right)+F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = F_{12}\! \left(x \right) F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = F_{128}\! \left(x \right)+F_{25}\! \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_28(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_6(x))
Eq(F_14(x), F_15(x) + F_16(x) + F_20(x))
Eq(F_15(x), 0)
Eq(F_16(x), F_12(x)*F_17(x))
Eq(F_17(x), F_18(x) + F_19(x))
Eq(F_18(x), F_10(x))
Eq(F_19(x), F_14(x))
Eq(F_20(x), F_12(x)*F_21(x))
Eq(F_21(x), F_22(x) + F_25(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_12(x)*F_24(x))
Eq(F_24(x), F_1(x) + F_22(x))
Eq(F_25(x), F_15(x) + F_20(x) + F_26(x))
Eq(F_26(x), F_12(x)*F_27(x))
Eq(F_27(x), F_10(x) + F_25(x))
Eq(F_28(x), F_29(x) + F_6(x))
Eq(F_29(x), F_15(x) + F_30(x) + F_98(x))
Eq(F_30(x), F_12(x)*F_31(x))
Eq(F_31(x), F_32(x) + F_54(x))
Eq(F_32(x), F_33(x) + F_6(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_12(x)*F_35(x))
Eq(F_35(x), F_36(x) + F_39(x))
Eq(F_36(x), F_12(x) + F_37(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_12(x)*F_36(x))
Eq(F_39(x), F_40(x) + F_41(x))
Eq(F_40(x), F_34(x))
Eq(F_41(x), 2*F_15(x) + F_42(x) + F_46(x))
Eq(F_42(x), F_12(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_45(x))
Eq(F_44(x), F_37(x))
Eq(F_45(x), F_41(x))
Eq(F_46(x), F_12(x)*F_47(x))
Eq(F_47(x), F_48(x) + F_51(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_12(x)*F_50(x))
Eq(F_50(x), F_12(x) + F_48(x))
Eq(F_51(x), 2*F_15(x) + F_46(x) + F_52(x))
Eq(F_52(x), F_12(x)*F_53(x))
Eq(F_53(x), F_37(x) + F_51(x))
Eq(F_54(x), F_29(x) + F_55(x))
Eq(F_55(x), 2*F_15(x) + F_56(x) + F_60(x))
Eq(F_56(x), F_12(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_59(x))
Eq(F_58(x), F_33(x))
Eq(F_59(x), F_55(x))
Eq(F_60(x), F_12(x)*F_61(x))
Eq(F_61(x), F_62(x) + F_67(x))
Eq(F_62(x), F_63(x) + F_65(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_12(x)*F_22(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_12(x)*F_62(x))
Eq(F_67(x), F_68(x) + F_88(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_12(x)*F_70(x))
Eq(F_70(x), F_71(x) + F_74(x))
Eq(F_71(x), F_63(x) + F_72(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_12(x)*F_71(x))
Eq(F_74(x), F_68(x) + F_75(x))
Eq(F_75(x), 3*F_15(x) + F_76(x) + F_80(x))
Eq(F_76(x), F_12(x)*F_77(x))
Eq(F_77(x), F_78(x) + F_79(x))
Eq(F_78(x), F_72(x))
Eq(F_79(x), F_75(x))
Eq(F_80(x), F_12(x)*F_81(x))
Eq(F_81(x), F_82(x) + F_85(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_12(x)*F_84(x))
Eq(F_84(x), F_63(x) + F_82(x))
Eq(F_85(x), 3*F_15(x) + F_80(x) + F_86(x))
Eq(F_86(x), F_12(x)*F_87(x))
Eq(F_87(x), F_72(x) + F_85(x))
Eq(F_88(x), 3*F_15(x) + F_89(x) + F_93(x))
Eq(F_89(x), F_12(x)*F_90(x))
Eq(F_90(x), F_91(x) + F_92(x))
Eq(F_91(x), F_65(x))
Eq(F_92(x), F_88(x))
Eq(F_93(x), F_12(x)*F_94(x))
Eq(F_94(x), F_82(x) + F_95(x))
Eq(F_95(x), 3*F_15(x) + F_93(x) + F_96(x))
Eq(F_96(x), F_12(x)*F_97(x))
Eq(F_97(x), F_65(x) + F_95(x))
Eq(F_98(x), F_12(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_21(x))
Eq(F_100(x), F_101(x) + F_121(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_103(x)*F_12(x))
Eq(F_103(x), F_104(x) + F_107(x))
Eq(F_104(x), F_105(x) + F_22(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_104(x)*F_12(x))
Eq(F_107(x), F_101(x) + F_108(x))
Eq(F_108(x), F_109(x) + F_113(x) + 2*F_15(x))
Eq(F_109(x), F_110(x)*F_12(x))
Eq(F_110(x), F_111(x) + F_112(x))
Eq(F_111(x), F_105(x))
Eq(F_112(x), F_108(x))
Eq(F_113(x), F_114(x)*F_12(x))
Eq(F_114(x), F_115(x) + F_118(x))
Eq(F_115(x), F_116(x))
Eq(F_116(x), F_117(x)*F_12(x))
Eq(F_117(x), F_115(x) + F_22(x))
Eq(F_118(x), F_113(x) + F_119(x) + 2*F_15(x))
Eq(F_119(x), F_12(x)*F_120(x))
Eq(F_120(x), F_105(x) + F_118(x))
Eq(F_121(x), F_122(x) + F_126(x) + 2*F_15(x))
Eq(F_122(x), F_12(x)*F_123(x))
Eq(F_123(x), F_124(x) + F_125(x))
Eq(F_124(x), F_25(x))
Eq(F_125(x), F_121(x))
Eq(F_126(x), F_12(x)*F_127(x))
Eq(F_127(x), F_115(x) + F_128(x))
Eq(F_128(x), F_126(x) + F_129(x) + 2*F_15(x))
Eq(F_129(x), F_12(x)*F_130(x))
Eq(F_130(x), F_128(x) + F_25(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:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [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": [], "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": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 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, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 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, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", 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