OFFSET
0,2
COMMENTS
The Coxeter diagram is:
o
|
5|
|
o---o---o
(4 nodes, T-shaped, one edge carries label 5)
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Maxim Chapovalov, Dimitry Leites, and Rafael Stekolshchik, The Poincaré 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 of the hyperbolic Coxeter groups with finite volume of fundamental domains, Journal of Nonlinear Mathematical Physics 17.supp01 (2010): 169-215.
R. L. Worthington, The growth series of compact hyperbolic Coxeter groups, with 4 and 5 generators, Canad. Math. Bull. 41(2) (1998) 231-239
Index entries for linear recurrences with constant coefficients, signature (3,-4,4,-3,2,-2,3,-4,4,-3,1).
FORMULA
G.f.: (t^2 + 1)*(t + 1)*(t^3 + 1)*(t^5 + 1)/t1 where t1 = (t-1)*(t^10 - 2*t^9 + 2*t^8 - 2*t^7 + t^6 - t^5 + t^4 - 2*t^3 + 2*t^2 - 2*t + 1).
PROG
(PARI) Vec((1+x)^3*(1-x+x^2)*(1+x^2)*(1-x+x^2-x^3+x^4) / ((1-x)*(1-2*x+2*x^2-2*x^3+x^4-x^5+x^6-2*x^7+2*x^8-2*x^9+x^10)) + O(x^50)) \\ Colin Barker, Jan 01 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Dec 27 2015
STATUS
approved