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

Author

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

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A005021, A094256, A122588.

Programs

Magma

R:=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

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}]

Sage

def A122589_list(prec):
    P. = 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

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

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