A251749 9-step Fibonacci sequence starting with 0,0,0,0,1,0,0,0,0.

0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 4, 8, 16, 31, 62, 124, 248, 496, 991, 1980, 3956, 7904, 15792, 31553, 63044, 125964, 251680, 502864, 1004737, 2007494, 4011032, 8014160, 16012528, 31993503, 63923962, 127721960, 255192240, 509881616, 1018758495, 2035509496

Offset: 0

Author

Arie Bos, Dec 07 2014

Keywords

• nonn
• easy

Links

• Robert Price, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,1,1,1,1,1,1,1,1).

Crossrefs

Other 9-step Fibonacci sequences are A104144, A105755, A127193, A251746, A251747, A251748, A251750, A251751, A251752.

Cf. A255532 (Indices of primes in this sequence).

Programs

Mathematica

LinearRecurrence[Table[1, {9}], {0, 0, 0, 0, 1, 0, 0, 0, 0}, 44] (* Michael De Vlieger, Dec 09 2014 *)

Formula

a(n+9) = a(n)+a(n+1)+a(n+2)+a(n+3)+a(n+4)+a(n+5)+a(n+6)+a(n+7)+a(n+8).

G.f.: x^4*(-1+x+x^2+x^3+x^4)/(-1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9) . - R. J. Mathar, Mar 28 2025