A139763 a(n)=a(n-1)+a(n-2)+a(n-3)+2a(n-4) with a(n)=n+1 for n<=3.

1, 2, 3, 4, 11, 22, 43, 84, 171, 342, 683, 1364, 2731, 5462, 10923, 21844, 43691, 87382, 174763, 349524, 699051, 1398102, 2796203, 5592404, 11184811, 22369622

Offset

0,2

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

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

Formula

a(n+1)-2a(n)=period 4:repeat 0, -1, -2, 3.

O.g.f.: (x-1)*(2*x^2+2*x+1)/((2*x-1)(1+x)(x^2+1)). a(n) = A056594(n+3)+((-1)^n+2^(n+1))/3. - R. J. Mathar, May 22 2008

Mathematica

LinearRecurrence[{1, 1, 1, 2}, {1, 2, 3, 4}, 30] (* Harvey P. Dale, May 22 2021 *)

Prog

(PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; 2, 1, 1, 1]^n*[1; 2; 3; 4])[1, 1] \\ Charles R Greathouse IV, May 26 2026

Crossrefs

Sequence in context: A066347 A367807 A118596 * A037396 A037432 A357360

Adjacent sequences: A139760 A139761 A139762 * A139764 A139765 A139766

Keyword

nonn,easy

Author

Paul Curtz, May 20 2008

Extensions

More terms from R. J. Mathar, May 22 2008

Status

approved