A266337 Expansion of b(3)*b(4)/(1 - 2*x + x^5), where b(k) = (1-x^k)/(1-x).

1, 4, 11, 25, 52, 104, 204, 397, 769, 1486, 2868, 5532, 10667, 20565, 39644, 76420, 147308, 283949, 547333, 1055022, 2033624, 3919940, 7555931, 14564529, 28074036, 54114448, 104308956, 201061981, 387559433, 747044830, 1439975212, 2775641468

Offset: 0

Author

Bruno Berselli, Dec 27 2015

Keywords

• nonn
• easy

Comments

This is the Poincaré series [or Poincare series] for the quasi-Lannér diagram QL4_21 - see Table 7.8 in Maxim Chapovalov, Dimitry Leites and Rafael Stekolshchik (2009), or equivalently Table 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, page 31.
• 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, Volume 17, Supplement 1 (2010), page 186.
• Index entries for linear recurrences with constant coefficients, signature (2,0,0,0,-1).

Crossrefs

Cf. similar sequences listed in A265055.

Programs

Magma

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

Mathematica

CoefficientList[Series[(1 + x) (1 + x^2) (1 + x + x^2)/((1 - x) (1 - x - x^2 - x^3 - x^4)), {x, 0, 40}], x]

Formula

G.f.: (1 + x)*(1 + x^2)*(1 + x + x^2)/((1 - x)*(1 - x - x^2 - x^3 - x^4)).

a(n) = 2*a(n-1) - a(n-5) for n>5.