OFFSET
0,2
COMMENTS
This is the Poincaré series [or Poincare series] for the quasi-Lannér diagram QL4_19 - 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,-1,1,-1,1,0,-1,1,-1).
FORMULA
G.f.: (1 + x)^3*(1 - x + x^2)*(1 + x + x^2)*(1 - x + x^2 - x^3 + x^4)/((1 - x)*(1 - x - x^2 - x^4 - x^6 - x^7 - x^9)).
MATHEMATICA
CoefficientList[Series[(1 + x)^3 (1 - x + x^2) (1 + x + x^2) (1 - x + x^2 - x^3 + x^4)/((1 - x) (1 - x - x^2 - x^4 - x^6 - x^7 - x^9)), {x, 0, 40}], x]
PROG
(Magma) /* By definition: */ m:=40; R<x>:=PowerSeriesRing(Integers(), m); b:=func<k|(1-x^k)/(1-x)>; Coefficients(R!(b(2)*b(6)*b(10)/(1-x-x^2-x^4-x^5+x^11+x^12+x^14)));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Bruno Berselli, Dec 28 2015
STATUS
approved