OFFSET
1,2
COMMENTS
Essentially the same as A005025. - R. J. Mathar, Aug 02 2008
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
MathPuzzle, Chebyshev Polynomials.
Index entries for linear recurrences with constant coefficients, signature (9,-28,35,-15,1).
FORMULA
G.f.: x/(1 - 9*x + 28*x^2 - 35*x^3 + 15*x^4 - x^5).
MATHEMATICA
m = 10; 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) I:=[1, 9, 53, 260, 1156]; [n le 5 select I[n] else 9*Self(n-1) -28*Self(n-2) +35*Self(n-3) -15*Self(n-4) +Self(n-5): n in [1..30]]; // G. C. Greubel, Nov 29 2021
(Sage)
def A122588_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( x/(1-9*x+28*x^2-35*x^3+15*x^4-x^5) ).list()
a=A122588_list(31); a[1:] # G. C. Greubel, Nov 29 2021
CROSSREFS
KEYWORD
nonn,easy,less
AUTHOR
Roger L. Bagula and Gary W. Adamson, Sep 19 2006
EXTENSIONS
Generating function corrected by R. J. Mathar, Jul 09 2009
New name (using g.f.) and editing by Joerg Arndt, Feb 12 2015
STATUS
approved