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Poincaré series [or Poincare series] P(C_{4,2}(0); t).
1

%I #22 Mar 15 2024 09:49:55

%S 1,0,3,4,12,14,42,56,126,182,360,532,972,1432,2452,3636,5902,8654,

%T 13560,19664,29810,42714,63056,89172,128716,179604,254176,350284,

%U 487084,663006,907866,1221456,1649213,2194634,2925833,3853200,5077908,6622158,8634634,11157700,14406370,18455400

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

%H Dragomir Z. Djokovic, <a href="http://arXiv.org/abs/math.AC/0609262">Poincaré series [or Poincare series] of some pure and mixed trace algebras of two generic matrices</a>. See Table 9.

%H <a href="/index/Rec#order_44">Index entries for linear recurrences with constant coefficients</a>, 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).

%F 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

%o (Sage)

%o def a(n):

%o if n==0: return 1

%o f = (1-x^2+x^4)*(1-x-x^3+x^4+2*x^5+x^6-x^7-x^9+x^10)

%o g = (1-x)*(1-x^2)^4*(1-x^3)^5*(1-x^4)^5

%o return (f/g).taylor(x, 0, n).coefficient(x^n) # _Robin Visser_, Mar 13 2024

%Y Cf. A124612.

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_, Dec 21 2006

%E More terms from _Robin Visser_, Mar 13 2024