A251748 9-step Fibonacci sequence starting with 0,0,0,0,0,1,0,0,0.

0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 4, 8, 16, 32, 63, 126, 252, 504, 1007, 2012, 4020, 8032, 16048, 32064, 64065, 128004, 255756, 511008, 1021009, 2040006, 4075992, 8143952, 16271856, 32511648, 64959231, 129790458, 259325160, 518139312, 1035257615, 2068475224

Offset: 0

Author

Arie Bos, Dec 07 2014

Keywords

• nonn
• easy

Comments

The only primes in this sequence whose indices are less than 2*10^5 are 2 and 65865769729, which correspond to indices of 10 and 45. - Robert Price, Feb 24 2015

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, A251749, A251750, A251751, A251752.

Programs

Mathematica

LinearRecurrence[Table[1, {9}], {0, 0, 0, 0, 0, 1, 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^5*(-1+x+x^2+x^3)/(-1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9) . - R. J. Mathar, Mar 28 2025