A266333 G.f. = b(2)*b(4)*b(6)/(x^8+x^6-x^5-x^3-x+1), where b(k) = (1-x^k)/(1-x).

1, 4, 9, 17, 29, 47, 74, 113, 170, 253, 375, 555, 818, 1203, 1767, 2594, 3807, 5584, 8188, 12004, 17597, 25795, 37809, 55416, 81220, 119038, 174464, 255694, 374742, 549215, 804918, 1179670, 1728895, 2533823, 3713502, 5442406, 7976239, 11689751, 17132167

Offset

0,2

Comments

This is the Poincaré series [or Poincare series] for the quasi-Lannér diagram QL4_2 - 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 (1,0,1,0,1,-1,0,-1).

Formula

G.f.: (1+x)^3*(1-x+x^2)*(1+x^2)*(1+x+x^2) / ((1-x)*(1-x-x^3)*(1+x+x^2+x^3+x^4)). - Colin Barker, Dec 29 2015

Maple

gf:= b(2)*b(4)*b(6)/(x^8+x^6-x^5-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^3 - x + 1), {x, 0, 40}], x] (* Bruno Berselli, Dec 29 2015 *)

Prog

(Magma) /* By definition: */ m:=40; R<x>:=PowerSeriesRing(Integers(), m); b:=func<k|(1-x^k)/(1-x)>; Coefficients(R!(b(2)*b(4)*b(6)/(x^8+x^6-x^5-x^3-x+1))); // Bruno Berselli, Dec 29 2015
(PARI) Vec((1+x)^3*(1-x+x^2)*(1+x^2)*(1+x+x^2) / ((1-x)*(1-x-x^3)*(1+x+x^2+x^3+x^4)) + O(x^50)) \\ Colin Barker, Dec 29 2015

Crossrefs

Cf. similar sequences listed in A265055.

Sequence in context: A266338 A301124 A265049 * A008225 A057313 A008127

Adjacent sequences: A266330 A266331 A266332 * A266334 A266335 A266336

Keyword

nonn,easy

Author

Alois P. Heinz, Dec 27 2015

Status

approved