OFFSET
0,2
COMMENTS
The Coxeter diagram is:
o---o
|...|
|...| 5
|...|
o---o
(4 nodes, square, 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,-3,1,2,-4,4,-2,-1,3,-3,1).
FORMULA
G.f.: -b(4)*(x^3+1)*(x^5+1)/t1 where b(k) = (1-x^k)/(1-x) and t1 = (x-1)*(x^10 - 2*x^9 + x^8 - 2*x^6 + 2*x^5 - 2*x^4 + x^2 - 2*x + 1).
G.f.: (1+x)^3*(1-x+x^2)*(1+x^2)*(1-x+x^2-x^3+x^4) / ((1-x)*(1-2*x+x^2-2*x^4+2*x^5-2*x^6+x^8-2*x^9+x^10)). - Colin Barker, Jan 01 2016
MATHEMATICA
Join[{1}, LinearRecurrence[{3, -3, 1, 2, -4, 4, -2, -1, 3, -3, 1}, {4, 10, 21, 40, 73, 130, 228, 396, 684, 1178, 2025}, 60]] (* Vincenzo Librandi, Jan 01 2016 *)
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+x^2-2*x^4+2*x^5-2*x^6+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