A266340 G.f. = b(2)*b(4)*b(6)/(x^8+x^6-x^5+x^4-2*x^3-x+1), where b(k) = (1-x^k)/(1-x).

1, 4, 9, 18, 33, 56, 93, 151, 241, 383, 606, 956, 1506, 2369, 3724, 5852, 9193, 14439, 22676, 35609, 55916, 87801, 137865, 216473, 339899, 533696, 837986, 1315766, 2065951, 3243852, 5093330, 7997283, 12556917, 19716214, 30957365, 48607628, 76321141, 119835439

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_8 - 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,-1,1,-1,1,-1).

Crossrefs

Cf. similar sequences listed in A265055.

Programs

Maple

gf:= b(2)*b(4)*b(6)/(x^8+x^6-x^5+x^4-2*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^6 - x^5 + x^4 - 2 x^3 - x + 1), {x, 0, 40}], x] (* Bruno Berselli, Dec 28 2015 *)