A266372 G.f. = b(2)*b(4)*b(6)/(x^9+x^8+x^7+x^6-x^5-x^4-x^3-x^2-x+1), where b(k) = (1-x^k)/(1-x).

1, 4, 10, 22, 45, 90, 177, 344, 666, 1286, 2482, 4788, 9232, 17798, 34309, 66136, 127485, 245738, 473678, 913046, 1759956, 3392428, 6539118, 12604558, 24296069, 46832182, 90271937, 174004756, 335404954, 646513838, 1246195494, 2402119052, 4630233348, 8925061742

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_11 - 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,-1,-1,-1,-1).

Crossrefs

Cf. similar sequences listed in A265055.

Programs

Magma

/* By definition: */ m:=40; R:=PowerSeriesRing(Integers(), m); b:=func; Coefficients(R!(b(2)*b(4)*b(6)/(x^9+x^8+x^7+x^6-x^5-x^4-x^3-x^2-x+1))); // Bruno Berselli, Dec 29 2015

Maple

gf:= b(2)*b(4)*b(6)/(x^9+x^8+x^7+x^6-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] b[4] b[6]/(x^9 + x^8 + x^7 + x^6 - x^5 - x^4 - x^3 - x^2 - x + 1), {x, 0, 40}], x] (* Bruno Berselli, Dec 28 2015 *)