login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A265053 Poincare series for hyperbolic reflection group with Coxeter diagram shown in Comments. 1
1, 4, 10, 21, 40, 73, 130, 228, 396, 684, 1178, 2025, 3476, 5961, 10218, 17512, 30010, 51424, 88114, 150977, 258684, 443225, 759410, 1301148, 2229340, 3819668, 6544474, 11213049, 19212000, 32917085, 56398834, 96631532, 165564642, 283671900, 486032194, 832748301, 1426797936, 2444619033 (list; graph; refs; listen; history; text; internal format)
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 [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,-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

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

Sequence in context: A144897 A001891 A266355 * A266371 A293823 A266354

Adjacent sequences:  A265050 A265051 A265052 * A265054 A265055 A265056

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Dec 27 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 21 16:04 EST 2019. Contains 329371 sequences. (Running on oeis4.)