A139800 a(n) = a(n-1) + a(n-2) + a(n-3) + 2*a(n-4), with a(0) = 1 and a(1) = a(2) = a(3) = 0.

1, 0, 0, 0, 2, 2, 4, 8, 18, 34, 68, 136, 274, 546, 1092, 2184, 4370, 8738, 17476, 34952, 69906, 139810, 279620, 559240, 1118482, 2236962, 4473924, 8947848, 17895698, 35791394, 71582788, 143165576, 286331154, 572662306, 1145324612, 2290649224, 4581298450, 9162596898

Offset

0,5

Links

Paolo Xausa, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,1,1,2).

Formula

From R. J. Mathar, Jun 12 2008: (Start)

O.g.f: (-1+x+x^2+x^3)/((2*x-1)(1+x)(1+x^2)).

a(n) = 2^n/15+(-1)^n/3+A112030(n)/5. (End)

Mathematica

LinearRecurrence[{1, 1, 1, 2}, {1, 0, 0, 0}, 50] (* Paolo Xausa, Jun 04 2026 *)

Prog

(PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; 2, 1, 1, 1]^n*[1; 0; 0; 0])[1, 1] \\ Charles R Greathouse IV, Jun 03 2026

Crossrefs

Cf. A112030.

Sequence in context: A063402 A175195 A369289 * A168058 A007971 A126068

Adjacent sequences: A139797 A139798 A139799 * A139801 A139802 A139803

Keyword

nonn,easy

Author

Paul Curtz, May 22 2008

Extensions

More terms from R. J. Mathar, Jun 12 2008

More terms from Paolo Xausa, Jun 04 2026

Status

approved