OFFSET
0,2
COMMENTS
The Coxeter diagram is:
..5
o---o
|...|
|...|
|...|
o---o
..4
(4 nodes, square, a pair of opposite edges carry labels 4 and 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,-3,2,0,-2,2,0,-2,3,-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^6+x^3+1)*(x^4-2*x^3+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^3+x^4)*(1+x^3+x^6)). - Colin Barker, Jan 01 2016
a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3) - 2*a(n-5) + 2*a(n-6) - 2*a(n-8) + 3*a(n-9) - 3*a(n-10) + a(n-11) for n>11. - Vincenzo Librandi, Jan 01 2016
MATHEMATICA
Join[{1}, LinearRecurrence[{3, -3, 2, 0, -2, 2, 0, -2, 3, -3, 1}, {4, 10, 22, 45, 89, 172, 328, 622, 1176, 2220, 4186}, 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^3+x^4)*(1+x^3+x^6)) + O(x^50)) \\ Colin Barker, Jan 01 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Dec 27 2015
STATUS
approved