0132_0231_1320_3012_3021
Counting sequence:
1, 1, 2, 6, 19, 53, 135, 334, 829, 2087, 5329, 13750, 35713, 93111, 243259, 636208, 1664795, 4357479, 11406799, 29861912, 78177749, 204669945, 535830473, 1402819616, 3672626249, 9615056713, 25172541155, 65902563674, 172535146419, 451702871737, 1182573464519, 3096017517090, 8105479081533, 21220419721771, 55555780077489, 145446920503818, 380784981426465, 996908023767419, 2609939089866939, 6832909245823812, 17888788647594139, 46833456696947435, 122611581443236143, 321001287632748076, 840392281454994229, 2200175556732219773, 5760134388741649225, 15080227609492710964, 39480548439736465609, 103361417709716666637, 270603704689413513859, 708449696358523853230, 1854745384386158022803, 4855786456799950190781, 12712613986013692523719, 33282055501241127353078, 87133552517709689506685, 228118602051887941136559, 597222253637954133870929, 1563548158861974460442462, 4093422222947969247420929, 10716718509981933281782975, 28056733306997830597888763, 73453481411011558511842136, 192303710926036844937594459, 503457651367098976300895983, 1318069243175260083965046095, 3450750078158681275594192704, 9034180991300783742817480149, 23651792895743669952858193537, 61921197695930226115757043849, 162111800192047008394412878920, 424414202880210799067481531273, 1111130808448585388808031650641, 2908978222465545367356613353699, 7615803858948050713261808340738, 19938433354378606772428811595955, 52199496204187769604024626371649, 136660055258184702039645067440519, 357780669570366336514910575868362, 936681953452914307505086660079869, 2452265190788376586000349404283315, 6420113618912215450495961552678833, 16808075665948269765487535253658546, 44004113378932593845966644208198689, 115204264470849511772412397370835843, 301608680033615941471270547904203515, 789621775629998312641399246341665644, 2067256646856378996452927191120680539, 5412148164939138676717382327020259187, 14169187847961037033699219789939976239, 37095415378943972424380277042799544660, 97117058288870880239441611338458528693, 254255759487668668293944556972575908101, 665650220174135124642392059579269057929, 1742694901034736705633231621765231123548, 4562434482930074992257302805716424166025, 11944608547755488271138676795384041223189, 31271391160336389821158727580435699347459, 81869564933253681192337505945923056658262, 214337303639424653755853790257333470461459
Generating function in Maple syntax:
-(x^8-3*x^7-x^6+6*x^5-8*x^4+15*x^3-14*x^2+6*x-1)/(x^2-3*x+1)/(x-1)^4
Generating function in latex syntax:
-\frac{x^{8}-3 x^{7}-x^{6}+6 x^{5}-8 x^{4}+15 x^{3}-14 x^{2}+6 x -1}{\left(x^{2}-3 x +1\right) \left(x -1\right)^{4}}
Generating function in sympy syntax:
(-x**8 + 3*x**7 + x**6 - 6*x**5 + 8*x**4 - 15*x**3 + 14*x**2 - 6*x + 1)/((x - 1)**4*(x**2 - 3*x + 1))
Implicit equation for the generating function in Maple syntax:
(x^2-3*x+1)*(x-1)^4*F(x)+x^8-3*x^7-x^6+6*x^5-8*x^4+15*x^3-14*x^2+6*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{2}-3 x +1\right) \left(x -1\right)^{4} F \! \left(x \right)+x^{8}-3 x^{7}-x^{6}+6 x^{5}-8 x^{4}+15 x^{3}-14 x^{2}+6 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,n = 2,2,1/30*(18*5^(1/2)-30)*(3/2-1/2*5^(1/2))^(-n)+1/30*(-18*5^(1/2)-30)*(3/2+1/2*5^(1/2))^(-n)+1/6*n^3+1/2*n^2-20/3*n+11)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ 2 & n =2 \\ \frac{\left(18 \sqrt{5}-30\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{30}+\frac{\left(-18 \sqrt{5}-30\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{30}+\frac{n^{3}}{6}+\frac{n^{2}}{2}-\\\frac{20 n}{3}+11 & \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) = 53
a(6) = 135
a(7) = 334
a(8) = 829
a(n+2) = -1/6*n^3-n^2-a(n)+3*a(n+1)+37/6*n-3, n >= 9
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) = 53
a \! \left(6\right) = 135
a \! \left(7\right) = 334
a \! \left(8\right) = 829
a \! \left(n +2\right) = -\frac{n^{3}}{6}-n^{2}-a \! \left(n \right)+3 a \! \left(n +1\right)+\frac{37 n}{6}-3, \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/19168/
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[36,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[13,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[4,x]
F[13,x] = F[14,x]+F[24,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[17,x]+F[18,x]
F[17,x] = F[1,x]+F[4,x]
F[18,x] = F[14,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[21,x]*F[4,x]
F[21,x] = F[22,x]+F[23,x]
F[22,x] = F[4,x]
F[23,x] = F[19,x]
F[24,x] = F[25,x]
F[25,x] = F[26,x]*F[4,x]
F[26,x] = F[27,x]+F[30,x]
F[27,x] = F[11,x]+F[28,x]
F[28,x] = F[29,x]
F[29,x] = F[11,x]*F[4,x]
F[30,x] = F[24,x]+F[31,x]
F[31,x] = F[32,x]
F[32,x] = F[33,x]*F[4,x]
F[33,x] = F[34,x]+F[35,x]
F[34,x] = F[28,x]
F[35,x] = F[31,x]
F[36,x] = F[37,x]+F[47,x]
F[37,x] = F[38,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[17,x]+F[40,x]
F[40,x] = F[37,x]+F[41,x]
F[41,x] = F[42,x]+F[43,x]+F[46,x]
F[42,x] = 0
F[43,x] = F[4,x]*F[44,x]
F[44,x] = F[22,x]+F[45,x]
F[45,x] = F[41,x]
F[46,x] = F[37,x]*F[4,x]
F[47,x] = F[42,x]+F[48,x]+F[94,x]
F[48,x] = F[4,x]*F[49,x]
F[49,x] = F[50,x]+F[60,x]
F[50,x] = F[51,x]+F[7,x]
F[51,x] = F[29,x]+F[42,x]+F[52,x]
F[52,x] = F[4,x]*F[53,x]
F[53,x] = F[54,x]+F[55,x]
F[54,x] = F[28,x]+F[4,x]
F[55,x] = F[56,x]+F[58,x]
F[56,x] = F[57,x]
F[57,x] = x^2
F[58,x] = F[59,x]
F[59,x] = F[28,x]*F[4,x]
F[60,x] = F[47,x]+F[61,x]
F[61,x] = F[42,x]+F[62,x]+F[66,x]+F[92,x]
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[64,x]+F[65,x]
F[64,x] = F[51,x]
F[65,x] = F[61,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = F[42,x]+F[68,x]+F[90,x]
F[68,x] = F[4,x]*F[69,x]
F[69,x] = F[70,x]+F[73,x]
F[70,x] = F[11,x]+F[71,x]
F[71,x] = F[29,x]+F[42,x]+F[72,x]
F[72,x] = F[4,x]*F[54,x]
F[73,x] = F[67,x]+F[74,x]
F[74,x] = F[42,x]+F[66,x]+F[75,x]+F[79,x]
F[75,x] = F[4,x]*F[76,x]
F[76,x] = F[77,x]+F[78,x]
F[77,x] = F[71,x]
F[78,x] = F[74,x]
F[79,x] = F[4,x]*F[80,x]
F[80,x] = F[81,x]+F[85,x]
F[81,x] = F[82,x]
F[82,x] = F[4,x]*F[83,x]
F[83,x] = F[22,x]+F[84,x]
F[84,x] = F[81,x]
F[85,x] = F[86,x]
F[86,x] = F[4,x]*F[87,x]
F[87,x] = F[88,x]+F[89,x]
F[88,x] = F[28,x]
F[89,x] = F[85,x]
F[90,x] = F[4,x]*F[91,x]
F[91,x] = F[37,x]+F[67,x]
F[92,x] = F[4,x]*F[93,x]
F[93,x] = F[80,x]
F[94,x] = F[4,x]*F[95,x]
F[95,x] = F[91,x]+F[96,x]
F[96,x] = F[97,x]+F[98,x]
F[97,x] = F[82,x]
F[98,x] = F[86,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_{36}\! \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_{13}\! \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_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{24}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{18}\! \left(x \right)
F_{17}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{18}\! \left(x \right) = F_{14}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)
F_{22}\! \left(x \right) = F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = F_{19}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{30}\! \left(x \right)
F_{27}\! \left(x \right) = F_{11}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{30}\! \left(x \right) = F_{24}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{35}\! \left(x \right)
F_{34}\! \left(x \right) = F_{28}\! \left(x \right)
F_{35}\! \left(x \right) = F_{31}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{47}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{17}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{37}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{43}\! \left(x \right)+F_{46}\! \left(x \right)
F_{42}\! \left(x \right) = 0
F_{43}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{22}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{41}\! \left(x \right)
F_{46}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{47}\! \left(x \right) = F_{42}\! \left(x \right)+F_{48}\! \left(x \right)+F_{94}\! \left(x \right)
F_{48}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{60}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{7}\! \left(x \right)
F_{51}\! \left(x \right) = F_{29}\! \left(x \right)+F_{42}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{55}\! \left(x \right)
F_{54}\! \left(x \right) = F_{28}\! \left(x \right)+F_{4}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{58}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = x^{2}
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{60}\! \left(x \right) = F_{47}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{42}\! \left(x \right)+F_{62}\! \left(x \right)+F_{66}\! \left(x \right)+F_{92}\! \left(x \right)
F_{62}\! \left(x \right) = F_{4}\! \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_{51}\! \left(x \right)
F_{65}\! \left(x \right) = F_{61}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{42}\! \left(x \right)+F_{68}\! \left(x \right)+F_{90}\! \left(x \right)
F_{68}\! \left(x \right) = F_{4}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{73}\! \left(x \right)
F_{70}\! \left(x \right) = F_{11}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{29}\! \left(x \right)+F_{42}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{73}\! \left(x \right) = F_{67}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{42}\! \left(x \right)+F_{66}\! \left(x \right)+F_{75}\! \left(x \right)+F_{79}\! \left(x \right)
F_{75}\! \left(x \right) = F_{4}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{78}\! \left(x \right)
F_{77}\! \left(x \right) = F_{71}\! \left(x \right)
F_{78}\! \left(x \right) = F_{74}\! \left(x \right)
F_{79}\! \left(x \right) = F_{4}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)+F_{85}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{4}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{22}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{81}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{4}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)+F_{89}\! \left(x \right)
F_{88}\! \left(x \right) = F_{28}\! \left(x \right)
F_{89}\! \left(x \right) = F_{85}\! \left(x \right)
F_{90}\! \left(x \right) = F_{4}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{37}\! \left(x \right)+F_{67}\! \left(x \right)
F_{92}\! \left(x \right) = F_{4}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{80}\! \left(x \right)
F_{94}\! \left(x \right) = F_{4}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{91}\! \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_{82}\! \left(x \right)
F_{98}\! \left(x \right) = F_{86}\! \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_36(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_13(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_4(x))
Eq(F_13(x), F_14(x) + F_24(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_17(x) + F_18(x))
Eq(F_17(x), F_1(x) + F_4(x))
Eq(F_18(x), F_14(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x)*F_4(x))
Eq(F_21(x), F_22(x) + F_23(x))
Eq(F_22(x), F_4(x))
Eq(F_23(x), F_19(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_26(x)*F_4(x))
Eq(F_26(x), F_27(x) + F_30(x))
Eq(F_27(x), F_11(x) + F_28(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_11(x)*F_4(x))
Eq(F_30(x), F_24(x) + F_31(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_33(x)*F_4(x))
Eq(F_33(x), F_34(x) + F_35(x))
Eq(F_34(x), F_28(x))
Eq(F_35(x), F_31(x))
Eq(F_36(x), F_37(x) + F_47(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_17(x) + F_40(x))
Eq(F_40(x), F_37(x) + F_41(x))
Eq(F_41(x), F_42(x) + F_43(x) + F_46(x))
Eq(F_42(x), 0)
Eq(F_43(x), F_4(x)*F_44(x))
Eq(F_44(x), F_22(x) + F_45(x))
Eq(F_45(x), F_41(x))
Eq(F_46(x), F_37(x)*F_4(x))
Eq(F_47(x), F_42(x) + F_48(x) + F_94(x))
Eq(F_48(x), F_4(x)*F_49(x))
Eq(F_49(x), F_50(x) + F_60(x))
Eq(F_50(x), F_51(x) + F_7(x))
Eq(F_51(x), F_29(x) + F_42(x) + F_52(x))
Eq(F_52(x), F_4(x)*F_53(x))
Eq(F_53(x), F_54(x) + F_55(x))
Eq(F_54(x), F_28(x) + F_4(x))
Eq(F_55(x), F_56(x) + F_58(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), x**2)
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_28(x)*F_4(x))
Eq(F_60(x), F_47(x) + F_61(x))
Eq(F_61(x), F_42(x) + F_62(x) + F_66(x) + F_92(x))
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_64(x) + F_65(x))
Eq(F_64(x), F_51(x))
Eq(F_65(x), F_61(x))
Eq(F_66(x), F_4(x)*F_67(x))
Eq(F_67(x), F_42(x) + F_68(x) + F_90(x))
Eq(F_68(x), F_4(x)*F_69(x))
Eq(F_69(x), F_70(x) + F_73(x))
Eq(F_70(x), F_11(x) + F_71(x))
Eq(F_71(x), F_29(x) + F_42(x) + F_72(x))
Eq(F_72(x), F_4(x)*F_54(x))
Eq(F_73(x), F_67(x) + F_74(x))
Eq(F_74(x), F_42(x) + F_66(x) + F_75(x) + F_79(x))
Eq(F_75(x), F_4(x)*F_76(x))
Eq(F_76(x), F_77(x) + F_78(x))
Eq(F_77(x), F_71(x))
Eq(F_78(x), F_74(x))
Eq(F_79(x), F_4(x)*F_80(x))
Eq(F_80(x), F_81(x) + F_85(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_4(x)*F_83(x))
Eq(F_83(x), F_22(x) + F_84(x))
Eq(F_84(x), F_81(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_4(x)*F_87(x))
Eq(F_87(x), F_88(x) + F_89(x))
Eq(F_88(x), F_28(x))
Eq(F_89(x), F_85(x))
Eq(F_90(x), F_4(x)*F_91(x))
Eq(F_91(x), F_37(x) + F_67(x))
Eq(F_92(x), F_4(x)*F_93(x))
Eq(F_93(x), F_80(x))
Eq(F_94(x), F_4(x)*F_95(x))
Eq(F_95(x), F_91(x) + F_96(x))
Eq(F_96(x), F_97(x) + F_98(x))
Eq(F_97(x), F_82(x))
Eq(F_98(x), F_86(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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[[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": 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"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]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}], "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": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 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