A130567 Expansion of x*(2 - 7*x + 2*x^2)/((1-x)*(1-4*x)*(1-2*x)).

2, 7, 23, 79, 287, 1087, 4223, 16639, 66047, 263167, 1050623, 4198399, 16785407, 67125247, 268468223, 1073807359, 4295098367, 17180131327, 68720001023, 274878955519, 1099513724927, 4398050705407, 17592194433023, 70368760954879

Offset

1,1

Links

Table of n, a(n) for n=1..24.

Formula

a(n) = 2^(2*n - 1) + 2*a(n - 1) + 1.

From R. J. Mathar, Jun 13 2008: (Start)

O.g.f.: x*(2 - 7*x + 2*x^2)/((1-x)*(1-4*x)*(1-2*x)).

a(n) = A093069(n-2), n>1. (End)

Mathematica

f[n_Integer?Positive] := f[n] = 2^(2*n - 1) + 2*f[n - 1] + 1; f[0] = 2; Table[f[n], {n, 0, 30}]
CoefficientList[Series[x*(2-7x+2x^2)/((1-x)(1-4x)(1-2x)), {x, 0, 30}], x] (* Harvey P. Dale, Sep 07 2015 *)

Crossrefs

Cf. A099393, A028244.

Sequence in context: A328035 A112657 A007717 * A091514 A143629 A176287

Adjacent sequences: A130564 A130565 A130566 * A130568 A130569 A130570

Keyword

nonn,easy

Author

Roger L. Bagula, Aug 09 2007

Extensions

New name from Joerg Arndt, Feb 08 2015

Status

approved