A266333 G.f. = b(2)*b(4)*b(6)/(x^8+x^6-x^5-x^3-x+1), where b(k) = (1-x^k)/(1-x).
1, 4, 9, 17, 29, 47, 74, 113, 170, 253, 375, 555, 818, 1203, 1767, 2594, 3807, 5584, 8188, 12004, 17597, 25795, 37809, 55416, 81220, 119038, 174464, 255694, 374742, 549215, 804918, 1179670, 1728895, 2533823, 3713502, 5442406, 7976239, 11689751, 17132167
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 (1,0,1,0,1,-1,0,-1).
Crossrefs
Cf. similar sequences listed in A265055.
Programs
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Magma
/* By definition: */ m:=40; R
:=PowerSeriesRing(Integers(), m); b:=func -
Maple
gf:= b(2)*b(4)*b(6)/(x^8+x^6-x^5-x^3-x+1): b:= k->(1-x^k)/(1-x): a:= n-> coeff(series(gf, x, n+1), x, n): seq(a(n), n=0..40);
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Mathematica
b[k_] := (1 - x^k)/(1 - x); CoefficientList[Series[b[2] b[4] b[6]/(x^8 + x^6 - x^5 - x^3 - x + 1), {x, 0, 40}], x] (* Bruno Berselli, Dec 29 2015 *) -
PARI
Vec((1+x)^3*(1-x+x^2)*(1+x^2)*(1+x+x^2) / ((1-x)*(1-x-x^3)*(1+x+x^2+x^3+x^4)) + O(x^50)) \\ Colin Barker, Dec 29 2015
Formula
G.f.: (1+x)^3*(1-x+x^2)*(1+x^2)*(1+x+x^2) / ((1-x)*(1-x-x^3)*(1+x+x^2+x^3+x^4)). - Colin Barker, Dec 29 2015
Comments