A272642 Expansion of (x^4+x^3+x^2-x-1)/(x^4+2*x^3+2*x^2+x-1).

1, 2, 3, 8, 18, 42, 97, 225, 521, 1207, 2796, 6477, 15004, 34757, 80515, 186514, 432062, 1000877, 2318544, 5370936, 12441840, 28821677, 66765773, 154663743, 358280483, 829961192, 1922615417, 4453762510, 10317196211, 23899913257, 55364446116, 128252427562, 297098342519, 688232003132

Offset: 0

Author

N. J. A. Sloane, May 07 2016

Keywords

• nonn
• easy

References

• Based on a suggestion of Wolfdieter Lang in A272362.

Links

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

Crossrefs

A272362 gives partial sums.

Programs

Magma

m:=40; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((x^4+x^3+x^2-x-1)/(x^4+2*x^3+2*x^2+x-1))); // Bruno Berselli, May 08 2016

Mathematica

CoefficientList[Series[(x^4 + x^3 + x^2 - x - 1)/(x^4 + 2 x^3 + 2 x^2 + x - 1), {x, 0, 40}], x] (* Vincenzo Librandi, May 08 2016 *)
LinearRecurrence[{1,2,2,1},{1,2,3,8,18},40] (* Harvey P. Dale, Oct 31 2024 *)

Formula

G.f.: (x^4+x^3+x^2-x-1)/(x^4+2*x^3+2*x^2+x-1).

a(n) = 2*a(n-1) + a(n-2) - a(n-4) - a(n-5). - Vincenzo Librandi, May 08 2016