A251656 4-step Fibonacci sequence starting with 1,0,1,0.

1, 0, 1, 0, 2, 3, 6, 11, 22, 42, 81, 156, 301, 580, 1118, 2155, 4154, 8007, 15434, 29750, 57345, 110536, 213065, 410696, 791642, 1525939, 2941342, 5669619, 10928542, 21065442, 40604945, 78268548, 150867477, 290806412, 560547382, 1080489819

Offset: 0

Author

Arie Bos, Dec 06 2014

Keywords

• nonn
• easy

Links

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

Crossrefs

Other 4-step Fibonacci sequences are A000078, A000288, A001630, A001631, A001648, A073817, A100532, A251654, A251655, A251703, A251704, A251705.

Cf. A000336.

Programs

J

NB. see A251655 for the program and apply it to 1,0,1,0.

Mathematica

LinearRecurrence[Table[1, {4}], {1, 0, 1, 0}, 36] (* Michael De Vlieger, Dec 09 2014 *)

Formula

a(n+4) = a(n)+a(n+1)+a(n+2)+a(n+3).

G.f.: (-1+x+2*x^3)/(-1+x+x^2+x^3+x^4) . - R. J. Mathar, Mar 28 2025

a(n) = A000078(n+3)-A000078(n+2)-2*A000078(n). - R. J. Mathar, Mar 28 2025