A266339 G.f. = b(2)^2*b(4)/(x^5+x^4-x^3-x^2-x+1), where b(k) = (1-x^k)/(1-x).

1, 4, 9, 18, 33, 56, 94, 156, 255, 416, 677, 1098, 1780, 2884, 4669, 7558, 12233, 19796, 32034, 51836, 83875, 135716, 219597, 355318, 574920, 930244, 1505169, 2435418, 3940593, 6376016, 10316614, 16692636, 27009255, 43701896, 70711157, 114413058, 185124220

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_7 - 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 (1,1,1,-1,-1).

Crossrefs

Cf. similar sequences listed in A265055.

Programs

Maple

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