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

Author

Roger L. Bagula, Aug 09 2007

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (7,-14,8).

Crossrefs

Cf. A093069, A099393, A028244.

Programs

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 *)

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)

Extensions

New name from Joerg Arndt, Feb 08 2015