A124637 Poincaré series [or Poincare series] P(C_{4,2}(0); t).

1, 0, 3, 4, 12, 14, 42, 56, 126, 182, 360, 532, 972, 1432, 2452, 3636, 5902, 8654, 13560, 19664, 29810, 42714, 63056, 89172, 128716, 179604, 254176, 350284, 487084, 663006, 907866, 1221456, 1649213, 2194634, 2925833, 3853200, 5077908, 6622158, 8634634, 11157700, 14406370, 18455400

Offset

0,3

Links

Table of n, a(n) for n=0..41.

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 (1, 4, 1, -6, -19, -6, 31, 54, 31, -80, -145, -75, 120, 300, 176, -146, -434, -356, 126, 500, 490, 0, -490, -500, -126, 356, 434, 146, -176, -300, -120, 75, 145, 80, -31, -54, -31, 6, 19, 6, -1, -4, -1, 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)*(1-x^2)^4*(1-x^3)^5*(1-x^4)^5). - Robin Visser, Mar 13 2024

Prog

(Sage)
def a(n):
    if n==0: return 1
    f = (1-x^2+x^4)*(1-x-x^3+x^4+2*x^5+x^6-x^7-x^9+x^10)
    g = (1-x)*(1-x^2)^4*(1-x^3)^5*(1-x^4)^5
    return (f/g).taylor(x, 0, n).coefficient(x^n) # Robin Visser, Mar 13 2024

Crossrefs

Cf. A124612.

Sequence in context: A376979 A336612 A070287 * A352907 A047173 A116653

Adjacent sequences: A124634 A124635 A124636 * A124638 A124639 A124640

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 21 2006

Extensions

More terms from Robin Visser, Mar 13 2024

Status

approved