A266374 G.f. = b(2)*b(6)/(3*x^6-2*x^5-2*x+1), where b(k) = (1-x^k)/(1-x).

1, 4, 10, 22, 46, 96, 198, 404, 822, 1670, 3394, 6896, 14006, 28444, 57762, 117302, 238214, 483752, 982374, 1994940, 4051198, 8226918, 16706698, 33926888, 68896534, 139910644, 284121530, 576975702, 1171685086, 2379382576, 4831896838, 9812304804, 19926196422

Offset: 0

Author

Alois P. Heinz, Dec 28 2015

Keywords

• nonn
• easy

Comments

This is the Poincaré series [or Poincare series] for the quasi-Lannér diagram QL4_13 - 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 (2,0,0,0,2,-3).

Crossrefs

Cf. similar sequences listed in A265055.

Programs

Magma

/* By definition: */ m:=40; R:=PowerSeriesRing(Integers(), m); b:=func; Coefficients(R!(b(2)*b(6)/(3*x^6-2*x^5-2*x+1))); // Bruno Berselli, Dec 29 2015

Maple

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