A124612 Poincaré series [or Poincare series] P(C_{4,2}; x).

1, 2, 6, 14, 34, 68, 144, 276, 534, 974, 1774, 3106, 5410, 9146, 15334, 25158, 40884, 65264, 103204, 160808, 248222, 378350, 571534, 853890, 1264962, 1855638, 2700490, 3895626, 5577846, 7923072, 11176164, 15650712, 21774473, 30092868, 41337096, 56434524

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 3, lines 6 and 7, also Table 5, lines 3-7.

Index entries for linear recurrences with constant coefficients, signature (3, 1, -6, -4, -6, 26, 24, -14, -46, -88, 46, 135, 125, -15, -304, -198, 34, 366, 404, -108, -384, -480, 0, 480, 384, 108, -404, -366, -34, 198, 304, 15, -125, -135, -46, 88, 46, 14, -24, -26, 6, 4, 6, -1, -3, 1).

Formula

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

Mathematica

CoefficientList[Series[(1-x^2+x^4)*(1-x-x^3+x^4+2*x^5+x^6-x^7-x^9+x^10) / ((1-x)^3*(1-x^2)^4*(1-x^3)^5*(1-x^4)^5), {x, 0, 35}], x] (* Stefano Spezia, Mar 14 2024 *)

Crossrefs

Cf. A124637.

Sequence in context: A005380 A309536 A257557 * A230439 A184697 A124613

Adjacent sequences: A124609 A124610 A124611 * A124613 A124614 A124615

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 21 2006

Status

approved