OFFSET
0,2
COMMENTS
The Coxeter diagram is:
..4
o---o
|...|
|...|
|...|
o---o
..4
(4 nodes, square, two opposite edges carry label 4)
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 (2,0,-1,1,0,-2,1).
FORMULA
G.f.: -b(2)*b(4)*(x^3+1)/t1 where b(k) = (1-x^k)/(1-x) and t1 = (x-1)*(x^6-x^5-x^4-x^2-x+1).
G.f.: (1+x)^3*(1-x+x^2)*(1+x^2) / ((1-x)*(1-x-x^2-x^4-x^5+x^6)). - Colin Barker, Jan 01 2016
MATHEMATICA
Join[{1}, LinearRecurrence[{2, 0, -1, 1, 0, -2, 1}, {4, 10, 22, 44, 84, 156, 284}, 60]] (* Vincenzo Librandi, Jan 01 2016 *)
PROG
(PARI) Vec((1+x)^3*(1-x+x^2)*(1+x^2)/((1-x)*(1-x-x^2-x^4-x^5+x^6)) + O(x^50)) \\ Colin Barker, Jan 01 2016
(Magma) I:=[1, 4, 10, 22, 44, 84, 156, 284]; [n le 8 select I[n] else 2*Self(n-1)-Self(n-3)+Self(n-4)-2*Self(n-6)+Self(n-7): n in [1..50]]; // Vincenzo Librandi, Jan 01 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Dec 27 2015
STATUS
approved