A266338 G.f. = b(2)*b(4)*b(6)/(x^8-x^3-x+1), where b(k) = (1-x^k)/(1-x).

1, 4, 9, 17, 29, 46, 70, 104, 152, 219, 314, 449, 639, 907, 1286, 1821, 2576, 3643, 5150, 7277, 10281, 14524, 20515, 28975, 40923, 57795, 81620, 115266, 162780, 229876, 324627, 458432, 647385, 914217, 1291029, 1823148, 2574585, 3635738, 5134259, 7250412

Offset: 0

Author

Alois P. Heinz, Dec 27 2015

Keywords

• nonn
• easy

Comments

This is the Poincaré series [or Poincare series] for the quasi-Lannér diagram QL4_6 - 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 (1,0,1,0,0,0,0,-1).

Crossrefs

Cf. similar sequences listed in A265055.

Programs

Maple

gf:= b(2)*b(4)*b(6)/(x^8-x^3-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^8 - x^3 - x + 1), {x, 0, 40}], x] (* Bruno Berselli, Dec 28 2015 *)