A265055 Expansion of b(2)*b(4)*b(6)/(x^8-x^4-x+1), where b(k) = (1-x^k)/(1-x).
1, 4, 9, 16, 25, 37, 53, 74, 101, 135, 179, 237, 313, 411, 537, 700, 912, 1188, 1546, 2009, 2608, 3385, 4394, 5703, 7399, 9596, 12444, 16138, 20929, 27140, 35190, 45625, 59155, 76699, 99445, 128932, 167158, 216717, 280972, 364279, 472282, 612300, 793827, 1029174, 1334298
Offset: 0
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.
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,0,0,0,-1).
Crossrefs
Programs
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Magma
/* By definition: */ m:=50; R
:=PowerSeriesRing(Integers(), m); b:=func -
Mathematica
Join[{1, 4}, LinearRecurrence[{1, 0, 0, 1, 0, 0, 0, -1}, {9, 16, 25, 37, 53, 74, 101, 135}, 50]] (* Jean-François Alcover, Jan 08 2019 *)
Formula
G.f.: (1 + x^2)*(1 - x + x^2)*(1 + x + x^2)*(1 + x)^3/((1 - x)*(1 - x^4 - x^5 - x^6 - x^7)). [Bruno Berselli, Dec 28 2015]
Comments