A251712 7-step Fibonacci sequence starting with (0,0,0,1,0,0,0).

0, 0, 0, 1, 0, 0, 0, 1, 2, 4, 8, 15, 30, 60, 120, 239, 476, 948, 1888, 3761, 7492, 14924, 29728, 59217, 117958, 234968, 468048, 932335, 1857178, 3699432, 7369136, 14679055, 29240152, 58245336, 116022624, 231112913, 460368648, 917037864, 1826706592, 3638734129

Offset: 0

Author

Arie Bos, Dec 07 2014

Keywords

• nonn
• easy

Links

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

Crossrefs

Other 7-step Fibonacci sequences are A066178, A104621, A122189, A251710, A251711, A251713, A251714.

Programs

J

NB. see A251713 for the program and apply it to 0 0 0 1 0 0 0.

Mathematica

LinearRecurrence[Table[1, {7}], {0, 0, 0, 1, 0, 0, 0}, 40] (* Michael De Vlieger, Dec 09 2014 *)

Formula

a(n+7) = a(n) + a(n+1) + a(n+2) + a(n+3) + a(n+4) + a(n+5) + a(n+6).

G.f.: x^3*(-1+x+x^2+x^3)/(-1+x+x^2+x^3+x^4+x^5+x^6+x^7) . - R. J. Mathar, Mar 28 2025