A124631 Poincaré series [or Poincare series] P(C#_{4,2}; x).

1, 0, 3, 4, 20, 26, 101, 168, 445, 813, 1804, 3246, 6527, 11455, 21193, 36168, 63077, 104034, 173255, 277043, 443629, 689569, 1068616, 1618029, 2438122, 3605596, 5300598, 7674008, 11039330, 15676558, 22120111, 30867691, 42805706, 58792192, 80263432, 108650796

Offset

0,3

Links

Table of n, a(n) for n=0..35.

Dragomir Z. Djokovic, Poincaré series [or Poincare series] of some pure and mixed trace algebras of two generic matrices. See Table 7.

Index entries for linear recurrences with constant coefficients, signature (0, 3, 4, 1, -10, -16, -10, 13, 42, 42, 8, -53, -94, -78, 2, 108, 160, 118, -14, -151, -216, -151, 10, 165, 236, 165, 10, -151, -216, -151, -14, 118, 160, 108, 2, -78, -94, -53, 8, 42, 42, 13, -10, -16, -10, 1, 4, 3, 0, -1).

Formula

G.f. = (1+10*x^4+12*x^5+38*x^6+93*x^8+131*x^9+235*x^10+299*x^11+473*x^12+560*x^13+714*x^14+761*x^15+876*x^16+830*x^17+876*x^18+761*x^19+714*x^20+560*x^21+473*x^22+299*x^23+235*x^24+131*x^25+93*x^26+46*x^27+38*x^28+12*x^29+10*x^30+x^34+46*x^7)/((1-x^2)^3*(1-x^3)^4*(1-x^4)^4*(1-x^5)^2*(1-x^6)).

Mathematica

CoefficientList[Series[(1+10x^4+12x^5+38x^6+93x^8+131x^9+235x^10+299x^11+473x^12+560x^13+714x^14+761x^15+876x^16+830x^17+876x^18+761x^19+714x^20+560x^21+473x^22+299x^23+235x^24+131x^25+93x^26+46x^27+38x^28+12x^29+10x^30+x^34+46x^7)/((1-x^2)^3(1-x^3)^4(1-x^4)^4(1-x^5)^2(1-x^6)), {x, 0, 40}], x] (* or *) LinearRecurrence[ {0, 3, 4, 1, -10, -16, -10, 13, 42, 42, 8, -53, -94, -78, 2, 108, 160, 118, -14, -151, -216, -151, 10, 165, 236, 165, 10, -151, -216, -151, -14, 118, 160, 108, 2, -78, -94, -53, 8, 42, 42, 13, -10, -16, -10, 1, 4, 3, 0, -1}, {1, 0, 3, 4, 20, 26, 101, 168, 445, 813, 1804, 3246, 6527, 11455, 21193, 36168, 63077, 104034, 173255, 277043, 443629, 689569, 1068616, 1618029, 2438122, 3605596, 5300598, 7674008, 11039330, 15676558, 22120111, 30867691, 42805706, 58792192, 80263432, 108650796, 146238779, 195349646, 259543886, 342507386, 449688513, 586807417, 762073528, 984190432, 1265332030, 1618520444, 2061547569, 2613576998, 3300278494, 4149432584}, 40] (* Harvey P. Dale, Aug 11 2024 *)

Crossrefs

Sequence in context: A240970 A333320 A047165 * A262033 A062870 A226964

Adjacent sequences: A124628 A124629 A124630 * A124632 A124633 A124634

Keyword

nonn,changed

Author

N. J. A. Sloane, Dec 21 2006

Status

approved