OFFSET
0,2
COMMENTS
This is the Poincaré series [or Poincare series] for the quasi-Lannér diagram QL4_20 - 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,-2).
FORMULA
G.f.: (1 + x)^2*(1 - x + x^2)*(1 + x + x^2)/((1 - x)*(1 - x - x^2 - x^4 - 2*x^5)).
a(n) = 2*a(n-1) - a(n-3) + a(n-4) + a(n-5) - 2*a(n-6) for n>6.
MATHEMATICA
CoefficientList[Series[(1 + x)^2 (1 - x + x^2) (1 + x + x^2)/((1 - x) (1 - x - x^2 - x^4 - 2 x^5)), {x, 0, 40}], x]
LinearRecurrence[{2, 0, -1, 1, 1, -2}, {1, 4, 10, 21, 41, 79, 150}, 40] (* Harvey P. Dale, Jan 18 2021 *)
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)/(1-2*x+x^3-x^4-x^5+2*x^6)));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Bruno Berselli, Dec 28 2015
STATUS
approved