OFFSET
0,5
COMMENTS
The inverse binomial transform is {0, 0, 0, 1, 0, 2, 0, 5, 0, 12, 0, 29, ...} (n>=0), an aerated variant of A000129. - R. J. Mathar, Jul 10 2019
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-4,0,2).
FORMULA
G.f.: x^3 / (1-4*x+4*x^2-2*x^4). - Colin Barker, Apr 08 2016
MAPLE
seq(coeff(series(x^3/(1-4*x+4*x^2-2*x^4), x, n+1), x, n), n = 0 ..35); # G. C. Greubel, Nov 21 2019
MATHEMATICA
LinearRecurrence[{4, -4, 0, 2}, {0, 0, 0, 1}, 35] (* G. C. Greubel, Oct 04 2016 *)
PROG
(PARI) concat(vector(3), Vec(x^3/(1-4*x+4*x^2-2*x^4) + O(x^35))) \\ Colin Barker, Apr 08 2016
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( x^3/(1-4*x+4*x^2-2*x^4) )); // G. C. Greubel, Nov 21 2019
(Sage)
def A135248_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P(x^3/(1-4*x+4*x^2-2*x^4)).list()
A135248_list(30) # G. C. Greubel, Nov 21 2019
(GAP) a:=[0, 0, 0, 1];; for n in [5..35] do a[n]:=4*a[n-1]-4*a[n-2]+ 2*a[n-4]; od; a; # G. C. Greubel, Nov 21 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Feb 15 2008
STATUS
approved