0132_0213_0321_1230_3021
Counting sequence:
1, 1, 2, 6, 19, 55, 152, 412, 1107, 2959, 7878, 20904, 55311, 146009, 384710, 1012152, 2659861, 6983725, 18323978, 48053626, 125967837, 330111877, 864891912, 2265612246, 5934041769, 15540707135, 40696467992, 106565473782, 279033507487, 730602157219, 1912907181548, 5008387822504, 13112793156471, 34331065388299, 89882550491610, 235320881053332, 616088682602451, 1612962346622645, 4222832717003258, 11055604523863236, 28944118293539257, 75777025234660777, 198387507166256222, 519386595775734886, 1359774479184203169, 3559941239823384865, 9320058036378972732, 24400250461499576802, 63880728532491845517, 167242005504720136379, 437845428719156917868, 1146294562127727326754, 3001038820613978482531, 7856823025614114962239, 20569432508028180088160, 53851479002070052671412, 140985013505381232665691, 369103579528472154806215, 966325761108832250715438, 2529873775855618635266496, 6623295710573211730938327, 17340013644094392709258577, 45396745798170718700259182, 118850224903339267998364176, 311153931217690094508525469, 814611573361417033954598245, 2132680798089933044210043122, 5583430839355126172385080722, 14617611756868933620364300197, 38269404505038650983546024189, 100190601905820971919950183088, 262302401507572169955657348654, 686716603207191348305727512241, 1797847409294593495678936489079, 4706825627037772380165904559360, 12322629476541090127688422400142, 32261062812030230968638653065831, 84460558978439068709706117649435, 221120614161065907023436861589268, 578901283580316516086518790534656, 1515583236730999368687948156850047, 3967848426914913044880982973689027, 10387962044618202675762315351567042, 27196037708148620802020592255715116, 71200151082245511369528719764987419, 186404415543423616585024083738068525, 488013095557696744942460564846864162, 1277634871149009431356191677597819292, 3344891517928017175353782601537187777, 8757039682712413347160492394194935649, 22926227530363965371038367115410005958, 60021642908688967775775954020759859454, 157138701196321907975932185084319130601, 411394460681514696191305981507096652569, 1077044680850698060676556519986769071460, 2819739581875531245995505099552807054522, 7382174064785799197624241820870845081621, 19326782612501673387505786447458114173555, 50598173772758835046150249690300269409748, 132467738705854059913459226961036238001466, 346805042344961801019255959867995532490667
Generating function in Maple syntax:
-(2*x^7-6*x^6+6*x^5-14*x^4+24*x^3-19*x^2+7*x-1)/(2*x-1)/(x^2-3*x+1)/(x-1)^3
Generating function in latex syntax:
-\frac{2 x^{7}-6 x^{6}+6 x^{5}-14 x^{4}+24 x^{3}-19 x^{2}+7 x -1}{\left(2 x -1\right) \left(x^{2}-3 x +1\right) \left(x -1\right)^{3}}
Generating function in sympy syntax:
(-2*x**7 + 6*x**6 - 6*x**5 + 14*x**4 - 24*x**3 + 19*x**2 - 7*x + 1)/((x - 1)**3*(2*x - 1)*(x**2 - 3*x + 1))
Implicit equation for the generating function in Maple syntax:
(2*x-1)*(x^2-3*x+1)*(x-1)^3*F(x)+2*x^7-6*x^6+6*x^5-14*x^4+24*x^3-19*x^2+7*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right) \left(x^{2}-3 x +1\right) \left(x -1\right)^{3} F \! \left(x \right)+2 x^{7}-6 x^{6}+6 x^{5}-14 x^{4}+24 x^{3}-19 x^{2}+7 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,1/10*(-2*5^(1/2)+10)*(3/2-1/2*5^(1/2))^(-n)+1/10*(2*5^(1/2)+10)*(3/2+1/2*5^(1/2))^(-n)+1/2*n^2-5/2*n-2^(-1+n)+3)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ \frac{\left(-2 \sqrt{5}+10\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{10}+\frac{\left(2 \sqrt{5}+10\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{10}+\frac{n^{2}}{2}-\frac{5 n}{2}-\\2^{-1+n}+3 & \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) = 152
a(7) = 412
a(n+3) = 1/2*n^2-7*a(n+1)+5*a(n+2)+2*a(n)-5/2*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) = 152
a \! \left(7\right) = 412
a \! \left(n +3\right) = \frac{n^{2}}{2}-7 a \! \left(n +1\right)+5 a \! \left(n +2\right)+2 a \! \left(n \right)-\frac{5 n}{2}+1, \quad n \geq 8
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/18267/
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[19,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[12,x]
F[17,x] = F[18,x]
F[18,x] = F[12,x]*F[13,x]
F[19,x] = F[20,x]+F[50,x]
F[20,x] = F[21,x]
F[21,x] = F[12,x]*F[22,x]
F[22,x] = F[23,x]+F[26,x]
F[23,x] = F[1,x]+F[24,x]
F[24,x] = F[25,x]
F[25,x] = F[12,x]*F[16,x]
F[26,x] = F[20,x]+F[27,x]
F[27,x] = F[28,x]+F[29,x]+F[48,x]
F[28,x] = 0
F[29,x] = F[12,x]*F[30,x]
F[30,x] = F[31,x]+F[35,x]
F[31,x] = F[24,x]+F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[12,x]*F[34,x]
F[34,x] = F[12,x]
F[35,x] = F[27,x]+F[36,x]
F[36,x] = 2*F[28,x]+F[37,x]+F[41,x]
F[37,x] = F[12,x]*F[38,x]
F[38,x] = F[39,x]+F[40,x]
F[39,x] = F[32,x]
F[40,x] = F[36,x]
F[41,x] = F[12,x]*F[42,x]
F[42,x] = F[43,x]
F[43,x] = F[44,x]
F[44,x] = F[12,x]*F[45,x]
F[45,x] = F[46,x]+F[47,x]
F[46,x] = F[12,x]
F[47,x] = F[43,x]
F[48,x] = F[12,x]*F[49,x]
F[49,x] = F[20,x]+F[43,x]
F[50,x] = F[115,x]+F[28,x]+F[51,x]
F[51,x] = F[12,x]*F[52,x]
F[52,x] = F[53,x]+F[67,x]
F[53,x] = F[54,x]+F[6,x]
F[54,x] = F[28,x]+F[55,x]+F[60,x]
F[55,x] = F[12,x]*F[56,x]
F[56,x] = F[10,x]+F[57,x]
F[57,x] = F[58,x]
F[58,x] = F[12,x]*F[59,x]
F[59,x] = F[12,x]+F[57,x]
F[60,x] = F[12,x]*F[61,x]
F[61,x] = F[59,x]+F[62,x]
F[62,x] = F[63,x]+F[65,x]
F[63,x] = F[64,x]
F[64,x] = x^2
F[65,x] = F[66,x]
F[66,x] = F[12,x]*F[62,x]
F[67,x] = F[50,x]+F[68,x]
F[68,x] = F[113,x]+F[28,x]+F[69,x]+F[91,x]
F[69,x] = F[12,x]*F[70,x]
F[70,x] = F[71,x]+F[75,x]
F[71,x] = F[54,x]+F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[12,x]*F[74,x]
F[74,x] = F[57,x]
F[75,x] = F[68,x]+F[76,x]
F[76,x] = 2*F[28,x]+F[77,x]+F[81,x]+F[90,x]
F[77,x] = F[12,x]*F[78,x]
F[78,x] = F[79,x]+F[80,x]
F[79,x] = F[72,x]
F[80,x] = F[76,x]
F[81,x] = F[12,x]*F[82,x]
F[82,x] = F[83,x]
F[83,x] = 2*F[28,x]+F[84,x]+F[88,x]
F[84,x] = F[12,x]*F[85,x]
F[85,x] = F[86,x]+F[87,x]
F[86,x] = F[57,x]
F[87,x] = F[83,x]
F[88,x] = F[12,x]*F[89,x]
F[89,x] = F[43,x]+F[83,x]
F[90,x] = 0
F[91,x] = F[12,x]*F[92,x]
F[92,x] = F[83,x]+F[93,x]
F[93,x] = F[111,x]+F[28,x]+F[94,x]
F[94,x] = F[12,x]*F[95,x]
F[95,x] = F[96,x]+F[98,x]
F[96,x] = F[10,x]+F[97,x]
F[97,x] = F[28,x]+F[55,x]+F[58,x]
F[98,x] = F[93,x]+F[99,x]
F[99,x] = F[100,x]+F[28,x]+F[88,x]+F[91,x]
F[100,x] = F[101,x]*F[12,x]
F[101,x] = F[102,x]+F[104,x]
F[102,x] = F[103,x]+F[97,x]
F[103,x] = F[73,x]
F[104,x] = F[105,x]+F[99,x]
F[105,x] = 2*F[28,x]+F[106,x]+F[110,x]+F[81,x]
F[106,x] = F[107,x]*F[12,x]
F[107,x] = F[108,x]+F[109,x]
F[108,x] = F[103,x]
F[109,x] = F[105,x]
F[110,x] = 0
F[111,x] = F[112,x]*F[12,x]
F[112,x] = F[20,x]+F[93,x]
F[113,x] = F[114,x]*F[12,x]
F[114,x] = F[89,x]
F[115,x] = F[116,x]*F[12,x]
F[116,x] = F[112,x]+F[117,x]
F[117,x] = F[118,x]+F[119,x]
F[118,x] = F[44,x]
F[119,x] = 2*F[28,x]+F[120,x]+F[84,x]
F[120,x] = F[117,x]*F[12,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_{19}\! \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_{12}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{50}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{12}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{26}\! \left(x \right)
F_{23}\! \left(x \right) = F_{1}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{12}\! \left(x \right) F_{16}\! \left(x \right)
F_{26}\! \left(x \right) = F_{20}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{29}\! \left(x \right)+F_{48}\! \left(x \right)
F_{28}\! \left(x \right) = 0
F_{29}\! \left(x \right) = F_{12}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{35}\! \left(x \right)
F_{31}\! \left(x \right) = F_{24}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{12}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{12}\! \left(x \right)
F_{35}\! \left(x \right) = F_{27}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = 2 F_{28}\! \left(x \right)+F_{37}\! \left(x \right)+F_{41}\! \left(x \right)
F_{37}\! \left(x \right) = F_{12}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{40}\! \left(x \right)
F_{39}\! \left(x \right) = F_{32}\! \left(x \right)
F_{40}\! \left(x \right) = F_{36}\! \left(x \right)
F_{41}\! \left(x \right) = F_{12}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{12}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{47}\! \left(x \right)
F_{46}\! \left(x \right) = F_{12}\! \left(x \right)
F_{47}\! \left(x \right) = F_{43}\! \left(x \right)
F_{48}\! \left(x \right) = F_{12}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{20}\! \left(x \right)+F_{43}\! \left(x \right)
F_{50}\! \left(x \right) = F_{115}\! \left(x \right)+F_{28}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{12}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{67}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{6}\! \left(x \right)
F_{54}\! \left(x \right) = F_{28}\! \left(x \right)+F_{55}\! \left(x \right)+F_{60}\! \left(x \right)
F_{55}\! \left(x \right) = F_{12}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{10}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{12}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{12}\! \left(x \right)+F_{57}\! \left(x \right)
F_{60}\! \left(x \right) = F_{12}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{59}\! \left(x \right)+F_{62}\! \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) = x^{2}
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_{50}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{113}\! \left(x \right)+F_{28}\! \left(x \right)+F_{69}\! \left(x \right)+F_{91}\! \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_{75}\! \left(x \right)
F_{71}\! \left(x \right) = F_{54}\! \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_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{57}\! \left(x \right)
F_{75}\! \left(x \right) = F_{68}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = 2 F_{28}\! \left(x \right)+F_{77}\! \left(x \right)+F_{81}\! \left(x \right)+F_{90}\! \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_{80}\! \left(x \right)
F_{79}\! \left(x \right) = F_{72}\! \left(x \right)
F_{80}\! \left(x \right) = F_{76}\! \left(x \right)
F_{81}\! \left(x \right) = F_{12}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = 2 F_{28}\! \left(x \right)+F_{84}\! \left(x \right)+F_{88}\! \left(x \right)
F_{84}\! \left(x \right) = F_{12}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{87}\! \left(x \right)
F_{86}\! \left(x \right) = F_{57}\! \left(x \right)
F_{87}\! \left(x \right) = F_{83}\! \left(x \right)
F_{88}\! \left(x \right) = F_{12}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{43}\! \left(x \right)+F_{83}\! \left(x \right)
F_{90}\! \left(x \right) = 0
F_{91}\! \left(x \right) = F_{12}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{83}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{111}\! \left(x \right)+F_{28}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{12}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)+F_{98}\! \left(x \right)
F_{96}\! \left(x \right) = F_{10}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{28}\! \left(x \right)+F_{55}\! \left(x \right)+F_{58}\! \left(x \right)
F_{98}\! \left(x \right) = F_{93}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{28}\! \left(x \right)+F_{88}\! \left(x \right)+F_{91}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{12}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{104}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{97}\! \left(x \right)
F_{103}\! \left(x \right) = F_{73}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{99}\! \left(x \right)
F_{105}\! \left(x \right) = 2 F_{28}\! \left(x \right)+F_{106}\! \left(x \right)+F_{110}\! \left(x \right)+F_{81}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{12}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{109}\! \left(x \right)
F_{108}\! \left(x \right) = F_{103}\! \left(x \right)
F_{109}\! \left(x \right) = F_{105}\! \left(x \right)
F_{110}\! \left(x \right) = 0
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{12}\! \left(x \right)
F_{112}\! \left(x \right) = F_{20}\! \left(x \right)+F_{93}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{12}\! \left(x \right)
F_{114}\! \left(x \right) = F_{89}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right) F_{12}\! \left(x \right)
F_{116}\! \left(x \right) = F_{112}\! \left(x \right)+F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{119}\! \left(x \right)
F_{118}\! \left(x \right) = F_{44}\! \left(x \right)
F_{119}\! \left(x \right) = 2 F_{28}\! \left(x \right)+F_{120}\! \left(x \right)+F_{84}\! \left(x \right)
F_{120}\! \left(x \right) = F_{117}\! \left(x \right) F_{12}\! \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_19(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_12(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_12(x)*F_13(x))
Eq(F_19(x), F_20(x) + F_50(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_12(x)*F_22(x))
Eq(F_22(x), F_23(x) + F_26(x))
Eq(F_23(x), F_1(x) + F_24(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_12(x)*F_16(x))
Eq(F_26(x), F_20(x) + F_27(x))
Eq(F_27(x), F_28(x) + F_29(x) + F_48(x))
Eq(F_28(x), 0)
Eq(F_29(x), F_12(x)*F_30(x))
Eq(F_30(x), F_31(x) + F_35(x))
Eq(F_31(x), F_24(x) + F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_12(x)*F_34(x))
Eq(F_34(x), F_12(x))
Eq(F_35(x), F_27(x) + F_36(x))
Eq(F_36(x), 2*F_28(x) + F_37(x) + F_41(x))
Eq(F_37(x), F_12(x)*F_38(x))
Eq(F_38(x), F_39(x) + F_40(x))
Eq(F_39(x), F_32(x))
Eq(F_40(x), F_36(x))
Eq(F_41(x), F_12(x)*F_42(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_12(x)*F_45(x))
Eq(F_45(x), F_46(x) + F_47(x))
Eq(F_46(x), F_12(x))
Eq(F_47(x), F_43(x))
Eq(F_48(x), F_12(x)*F_49(x))
Eq(F_49(x), F_20(x) + F_43(x))
Eq(F_50(x), F_115(x) + F_28(x) + F_51(x))
Eq(F_51(x), F_12(x)*F_52(x))
Eq(F_52(x), F_53(x) + F_67(x))
Eq(F_53(x), F_54(x) + F_6(x))
Eq(F_54(x), F_28(x) + F_55(x) + F_60(x))
Eq(F_55(x), F_12(x)*F_56(x))
Eq(F_56(x), F_10(x) + F_57(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_12(x)*F_59(x))
Eq(F_59(x), F_12(x) + F_57(x))
Eq(F_60(x), F_12(x)*F_61(x))
Eq(F_61(x), F_59(x) + F_62(x))
Eq(F_62(x), F_63(x) + F_65(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), x**2)
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_12(x)*F_62(x))
Eq(F_67(x), F_50(x) + F_68(x))
Eq(F_68(x), F_113(x) + F_28(x) + F_69(x) + F_91(x))
Eq(F_69(x), F_12(x)*F_70(x))
Eq(F_70(x), F_71(x) + F_75(x))
Eq(F_71(x), F_54(x) + F_72(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_12(x)*F_74(x))
Eq(F_74(x), F_57(x))
Eq(F_75(x), F_68(x) + F_76(x))
Eq(F_76(x), 2*F_28(x) + F_77(x) + F_81(x) + F_90(x))
Eq(F_77(x), F_12(x)*F_78(x))
Eq(F_78(x), F_79(x) + F_80(x))
Eq(F_79(x), F_72(x))
Eq(F_80(x), F_76(x))
Eq(F_81(x), F_12(x)*F_82(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), 2*F_28(x) + F_84(x) + F_88(x))
Eq(F_84(x), F_12(x)*F_85(x))
Eq(F_85(x), F_86(x) + F_87(x))
Eq(F_86(x), F_57(x))
Eq(F_87(x), F_83(x))
Eq(F_88(x), F_12(x)*F_89(x))
Eq(F_89(x), F_43(x) + F_83(x))
Eq(F_90(x), 0)
Eq(F_91(x), F_12(x)*F_92(x))
Eq(F_92(x), F_83(x) + F_93(x))
Eq(F_93(x), F_111(x) + F_28(x) + F_94(x))
Eq(F_94(x), F_12(x)*F_95(x))
Eq(F_95(x), F_96(x) + F_98(x))
Eq(F_96(x), F_10(x) + F_97(x))
Eq(F_97(x), F_28(x) + F_55(x) + F_58(x))
Eq(F_98(x), F_93(x) + F_99(x))
Eq(F_99(x), F_100(x) + F_28(x) + F_88(x) + F_91(x))
Eq(F_100(x), F_101(x)*F_12(x))
Eq(F_101(x), F_102(x) + F_104(x))
Eq(F_102(x), F_103(x) + F_97(x))
Eq(F_103(x), F_73(x))
Eq(F_104(x), F_105(x) + F_99(x))
Eq(F_105(x), F_106(x) + F_110(x) + 2*F_28(x) + F_81(x))
Eq(F_106(x), F_107(x)*F_12(x))
Eq(F_107(x), F_108(x) + F_109(x))
Eq(F_108(x), F_103(x))
Eq(F_109(x), F_105(x))
Eq(F_110(x), 0)
Eq(F_111(x), F_112(x)*F_12(x))
Eq(F_112(x), F_20(x) + F_93(x))
Eq(F_113(x), F_114(x)*F_12(x))
Eq(F_114(x), F_89(x))
Eq(F_115(x), F_116(x)*F_12(x))
Eq(F_116(x), F_112(x) + F_117(x))
Eq(F_117(x), F_118(x) + F_119(x))
Eq(F_118(x), F_44(x))
Eq(F_119(x), F_120(x) + 2*F_28(x) + F_84(x))
Eq(F_120(x), F_117(x)*F_12(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": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 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": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 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": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 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], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "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": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 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, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 2, 1], "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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "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], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 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], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 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