A266334 G.f. = b(2)*b(6)*b(10)/(x^14+x^12-x^5-x^3-x+1), where b(k) = (1-x^k)/(1-x).

1, 4, 9, 17, 30, 51, 84, 135, 215, 341, 538, 846, 1328, 2082, 3262, 5108, 7997, 12519, 19595, 30668, 47996, 75112, 117546, 183950, 287864, 450478, 704950, 1103170, 1726339, 2701526, 4227582, 6615684, 10352789, 16200930, 25352598, 39673907, 62085111, 97156070

Offset

0,2

Comments

This is the Poincaré series [or Poincare series] for the quasi-Lannér diagram QL4_3 - 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 (1,0,1,0,1,0,0,0,0,0,0,-1,0,-1).

Maple

gf:= b(2)*b(6)*b(10)/(x^14+x^12-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[6] b[10]/(x^14 + x^12 - 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(6)*b(10)/(x^14+x^12-x^5-x^3-x+1))); // Bruno Berselli, Dec 29 2015

Crossrefs

Cf. similar sequences listed in A265055.

Sequence in context: A008093 A027374 A265048 * A157728 A266335 A301125

Adjacent sequences: A266331 A266332 A266333 * A266335 A266336 A266337

Keyword

nonn,easy

Author

Alois P. Heinz, Dec 27 2015

Status

approved