A266376 G.f. = b(2)*b(4)*b(6)/(x^9+x^8+x^7-2*x^3-x^2-x+1), where b(k) = (1-x^k)/(1-x).

1, 4, 10, 23, 49, 100, 202, 404, 804, 1598, 3173, 6297, 12494, 24786, 49168, 97532, 193466, 383759, 761221, 1509948, 2995110, 5941052, 11784572, 23375678, 46367597, 91973973, 182437998, 361880886, 717820720, 1423856868, 2824338058, 5602308519, 11112643065

Offset: 0

Author

Alois P. Heinz, Dec 28 2015

Keywords

• nonn
• easy

Comments

This is the Poincaré series [or Poincare series] for the quasi-Lannér diagram QL4_15 - see Tables 7.6, 7.7 and 7.8 in Maxim Chapovalov, Dimitry Leites and Rafael Stekolshchik (2009), or equivalently Tables 5 and 6 in the shorter version, Maxim Chapovalov, Dimitry Leites and Rafael Stekolshchik (2010).

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Maxim Chapovalov, Dimitry Leites, and Rafael Stekolshchik, The Poincaré series [or Poincare series] of the hyperbolic Coxeter groups with finite volume of fundamental domains, arXiv:0906.1596 [math.RT], 2009.
• Maxim Chapovalov, Dimitry Leites, and Rafael Stekolshchik, The Poincaré series [or Poincare series] of the hyperbolic Coxeter groups with finite volume of fundamental domains, Journal of Nonlinear Mathematical Physics 17.supp01 (2010), 169-215.
• Index entries for linear recurrences with constant coefficients, signature (2,0,0,0,0,0,-1).

Crossrefs

Cf. similar sequences listed in A265055.

Programs

Magma

/* By definition: */ m:=40; R:=PowerSeriesRing(Integers(), m); b:=func; Coefficients(R!(b(2)*b(4)*b(6)/(x^9+x^8+x^7-2*x^3-x^2-x+1))); // Bruno Berselli, Dec 29 2015

Maple

gf:= b(2)*b(4)*b(6)/(x^9+x^8+x^7-2*x^3-x^2-x+1):
b:= k->(1-x^k)/(1-x):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..40);

Mathematica

b[k_] := (1 - x^k)/(1 - x); CoefficientList[Series[b[2] b[4] b[6]/(x^9 + x^8 + x^7 - 2 x^3 - x^2 - x + 1), {x, 0, 40}], x] (* Bruno Berselli, Dec 28 2015 *)