A266336 G.f. = b(2)*b(6)/(x^6-x^4+x^2-2*x+1), where b(k) = (1-x^k)/(1-x).

1, 4, 9, 16, 26, 42, 67, 104, 158, 238, 359, 542, 816, 1224, 1833, 2746, 4116, 6168, 9237, 13828, 20702, 30998, 46415, 69492, 104034, 155746, 233171, 349090, 522628, 782420, 1171349, 1753622, 2625352, 3930412, 5884193, 8809176, 13188162, 19743938, 29558555

Offset: 0

Author

Alois P. Heinz, Dec 27 2015

Keywords

• nonn
• easy

Comments

This is the Poincaré series [or Poincare series] for the quasi-Lannér diagram QL4_5 - 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,-1,0,1,0,-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(6)/(x^6-x^4+x^2-2*x+1))); // Bruno Berselli, Dec 29 2015

Maple

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