A124636 Poincaré series [or Poincare series] P(C_{3,2}(0); t).

1, 0, 3, 4, 7, 12, 24, 28, 55, 76, 111, 160, 238, 304, 447, 588, 784, 1036, 1379, 1728, 2278, 2864, 3611, 4524, 5673, 6908, 8594, 10436, 12669, 15308, 18479, 21944, 26319, 31128, 36770, 43280, 50868, 59184, 69194, 80184, 92784, 107064, 123354, 141168, 161940, 184656, 210258, 238872, 270993

Offset

0,3

Links

Table of n, a(n) for n=0..48.

Dragomir Z. Djokovic, Poincaré series [or Poincare series] of some pure and mixed trace algebras of two generic matrices. See Table 9.

Index entries for linear recurrences with constant coefficients, signature (0,4,4,-6,-16,-2,24,23,-12,-36,-12,23,24,-2,-16,-6,4,4,0,-1).

Formula

G.f.: (1 - x^2 + x^4)/((1 - x^2)^4*(1 - x^3)^4). - Robin Visser, Mar 13 2024

Prog

(Sage)
def a(n):
    if n==0: return 1
    f = (1-x^2+x^4)/((1-x^2)^4*(1-x^3)^4)
    return f.taylor(x, 0, n).coefficient(x^n) # Robin Visser, Mar 13 2024

Crossrefs

Cf. A123991.

Sequence in context: A325851 A062202 A049859 * A231337 A373805 A049930

Adjacent sequences: A124633 A124634 A124635 * A124637 A124638 A124639

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 21 2006

Extensions

More terms from Robin Visser, Mar 13 2024

Status

approved