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A265054 Poincare series for hyperbolic reflection group with Coxeter diagram shown in Comments. 9
1, 4, 10, 22, 46, 94, 188, 372, 734, 1446, 2844, 5588, 10976, 21556, 42330, 83120, 163214, 320484, 629292, 1235652, 2426272, 4764118, 9354602, 18368260, 36067056, 70819582, 139058010, 273047782, 536143806, 1052746804, 2067124190, 4058907988, 7969881118, 15649284294, 30728199738, 60336449982 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The Coxeter diagram is:

..5

o---o

|...|

|...|

|...|

o---o

..5

(4 nodes, square, two opposite edges carry label 5)

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.

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 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,-2,-1,3,-3,1,2,-3,1).

FORMULA

G.f.: -b(2)*(x^3+1)*(x^5+1)/t1 where b(k) = (1-x^k)/(1-x) and t1 = (x-1)*(x^2+1)*(x^6-2*x^5-x^4+3*x^3-x^2-2*x+1).

G.f.: (1+x)^3*(1-x+x^2)*(1-x+x^2-x^3+x^4) / ((1-x)*(1+x^2)*(1-2*x-x^2+3*x^3-x^4-2*x^5+x^6)). - Colin Barker, Jan 01 2016

PROG

(PARI) Vec((1+x)^3*(1-x+x^2)*(1-x+x^2-x^3+x^4)/((1-x)*(1+x^2)*(1-2*x-x^2+3*x^3-x^4-2*x^5+x^6)) + O(x^40)) \\ Colin Barker, Jan 01 2016

CROSSREFS

Poincare series in this family: A265044 and A265047 - A265054.

Sequence in context: A174622 A038621 A078407 * A099018 A033484 A296953

Adjacent sequences:  A265051 A265052 A265053 * A265055 A265056 A265057

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Dec 27 2015

STATUS

approved

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Last modified October 21 11:15 EDT 2019. Contains 328294 sequences. (Running on oeis4.)