A291039 a(n) = (1/4)*A291038(n).

1, 3, 8, 21, 54, 136, 337, 825, 2000, 4809, 11484, 27264, 64401, 151455, 354808, 828349, 1927986, 4475080, 10361441, 23936565, 55183904, 126983569, 291698040, 669004352, 1532095329, 3503889147, 8003207912, 18258464741, 41608726254, 94722900936, 215428701233

Offset: 0

Author

Clark Kimberling, Sep 14 2017

Keywords

• nonn
• easy

Links

• Clark Kimberling, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4, -4, 2, -4, 0, -1)

Crossrefs

Cf. A079978, A290616, A291038.

Programs

Mathematica

z = 60; s = x/(x - x^3); p = (1 - 2 s)^2;
Drop[CoefficientList[Series[s, {x, 0, z}], x], 1]  (* A079978  *)
u = Drop[CoefficientList[Series[1/p, {x, 0, z}], x], 1]  (* A291038 *)
u/4 (* A291039 *)

Formula

G.f.: -((-1 + x + x^3)/(-1 + 2 x + x^3)^2).

a(n) = 4*a(n-1) - 4*a(n-2) + 2*a(n-3) - 4*a(n-4) - a(n-6) for n >= 7.