A266370 G.f. = b(2)^2*b(4)/(2*x^5+x^4-2*x^3-x^2-x+1), where b(k) = (1-x^k)/(1-x).

1, 4, 9, 19, 38, 70, 129, 238, 431, 781, 1419, 2566, 4640, 8401, 15192, 27469, 49691, 89863, 162498, 293890, 531485, 961126, 1738167, 3143377, 5684531, 10280146, 18591012, 33620509, 60800528, 109953853, 198844095, 359596471, 650306726, 1176036478, 2126784345

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_9 - 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 (1,1,2,-1,-2).

Crossrefs

Cf. similar sequences listed in A265055.

Programs

Magma

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

Maple

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