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
(SageMath)
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
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