A251713 7-step Fibonacci sequence starting with (0,0,1,0,0,0,0).

0, 0, 1, 0, 0, 0, 0, 1, 2, 4, 7, 14, 28, 56, 112, 223, 444, 884, 1761, 3508, 6988, 13920, 27728, 55233, 110022, 219160, 436559, 869610, 1732232, 3450544, 6873360, 13691487, 27272952, 54326744, 108216929, 215564248, 429396264, 855341984, 1703810608, 3393929729

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, A251712, A251714.

Programs

J

(see www.jsoftware.com) First construct the generating matrix
   [M=: (#.@}: + {:)\"1&.|: <:/~i.7
 1  1  1  1  1  1  1
 1  2  2  2  2  2  2
 2  3  4  4  4  4  4
 4  6  7  8  8  8  8
 8 12 14 15 16 16 16
16 24 28 30 31 32 32
32 48 56 60 62 63 64
Given that matrix, one can produce the first 7*150 numbers by
, M(+/ . *)^:(i.150) 0 0 1 0 0 0 0x

Mathematica

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