A135248 a(n) = 4*a(n-1) - 4*a(n-2) + 2*a(n-4), with a(0)=a(1)=a(2)=0, and a(3)=1.

0, 0, 0, 1, 4, 12, 32, 82, 208, 528, 1344, 3428, 8752, 22352, 57088, 145800, 372352, 950912, 2428416, 6201616, 15837504, 40445376, 103288320, 263775008, 673621760, 1720277760, 4393200640, 11219241536, 28651407104, 73169217792, 186857644032, 477192188032

Offset: 0

Author

Paul Curtz, Feb 15 2008

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A101893 (first differences).

Programs

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

Magma

R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( x^3/(1-4*x+4*x^2-2*x^4) )); // G. C. Greubel, Nov 21 2019

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 *)

PARI

concat(vector(3), Vec(x^3/(1-4*x+4*x^2-2*x^4) + O(x^35))) \\ Colin Barker, Apr 08 2016

Sage

def A135248_list(prec):
    P. = 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

Formula

G.f.: x^3 / (1-4*x+4*x^2-2*x^4). - Colin Barker, Apr 08 2016