A122589 Expansion of 1/(1 - 11*x + 45*x^2 - 84*x^3 + 70*x^4 - 21*x^5 + x^6).

1, 11, 76, 425, 2109, 9709, 42504, 179630, 740025, 2991495, 11920740, 46981740, 183579396, 712493461, 2750450981, 10572046555, 40495806764, 154683305139, 589504177384, 2242448706435, 8517201473375, 32309383853565

Offset

0,2

Comments

Previous name was: Sum_{n >= 0} a(n)*x^(2n) / 4^(n+6) = 1/(4096 - 11264*x^2 + 11520*x^4 - 5376*x^6 + 1120*x^8 - 84*x^10 + x^12).

Suggested by study of polynomials associated with the regular 13-gon.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (11,-45,84,-70,21,-1).

Formula

G.f.: 1/(1 - 11*x + 45*x^2 - 84*x^3 + 70*x^4 - 21*x^5 + x^6). - Colin Barker, Oct 16 2013

Maple

A122589:= proc(n) coeftayl(1/(4096-11264*x^2+11520*x^4-5376*x^6+1120*x^8-84*x^10 +x^12), x=0, 2*n); %*2^(2*n+12); end: seq(A122589(n), n=0..30); # R. J. Mathar, Sep 21 2007

Mathematica

m=12; p[x_]:= ExpandAll[x^m*ChebyshevU[m, 1/x]]; Table[ SeriesCoefficient[ Series[2^(n+m-1)*x/p[x], {x, 0, 30}], n], {n, 1, 30, 2}]

Prog

(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( 1/(1-11*x+45*x^2 -84*x^3+70*x^4-21*x^5+x^6) )); // G. C. Greubel, Nov 29 2021
(Sage)
def A122589_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( 1/(1-11*x+45*x^2-84*x^3+70*x^4-21*x^5+x^6) ).list()
A122589_list(30) # G. C. Greubel, Nov 29 2021

Crossrefs

Cf. A005021, A094256, A122588.

Sequence in context: A282816 A055901 A036427 * A302382 A034269 A256597

Adjacent sequences: A122586 A122587 A122588 * A122590 A122591 A122592

Keyword

nonn,easy

Author

Roger L. Bagula and Gary W. Adamson, Sep 19 2006

Extensions

Edited by N. J. A. Sloane, Oct 02 2006

More terms from R. J. Mathar, Sep 21 2007

New name from Colin Barker, Oct 16 2013

Status

approved