A124633 Poincaré series [or Poincare series] P(C^o_{3,2}; x).

1, 2, 9, 25, 66, 149, 329, 650, 1248, 2255, 3941, 6608, 10799, 17085, 26456, 39983, 59306, 86274, 123572, 174146, 242186, 332312, 450738, 604418, 802447, 1054848, 1374561, 1775839, 2276528, 2896401, 3659799, 4593424, 5729858, 7104777, 8760897, 10745098

Offset

0,2

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 8.

Index entries for linear recurrences with constant coefficients, signature (2, 2, -3, -5, -2, 11, 7, -5, -11, -9, 9, 11, 5, -7, -11, 2, 5, 3, -2, -2, 1).

Formula

G.f.: (x^12+3*x^10+6*x^9+9*x^8+6*x^7+12*x^6+6*x^5+9*x^4+6*x^3+3*x^2+1) / ((1-x)^2*(1-x^2)^3*(1-x^3)^3*(1-x^4)).

Mathematica

CoefficientList[Series[(x^12+3x^10+6x^9+9x^8+6x^7+12x^6+6x^5+9x^4+6x^3+3x^2+1)/((1-x)^2(1-x^2)^3(1-x^3)^3(1-x^4)), {x, 0, 40}], x] (* or *) LinearRecurrence[{2, 2, -3, -5, -2, 11, 7, -5, -11, -9, 9, 11, 5, -7, -11, 2, 5, 3, -2, -2, 1}, {1, 2, 9, 25, 66, 149, 329, 650, 1248, 2255, 3941, 6608, 10799, 17085, 26456, 39983, 59306, 86274, 123572, 174146, 242186}, 40] (* Harvey P. Dale, Apr 01 2023 *)

Crossrefs

Sequence in context: A173965 A116454 A295143 * A093122 A305351 A101051

Adjacent sequences: A124630 A124631 A124632 * A124634 A124635 A124636

Keyword

nonn

Author

N. J. A. Sloane, Dec 21 2006

Status

approved