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

0,9

Links

Table of n, a(n) for n=0..39.

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

Formula

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

Mathematica

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

Prog

(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

Crossrefs

Other 7-step Fibonacci sequences are A066178, A104621, A122189, A251710, A251711, A251712, A251714.

Sequence in context: A057744 A251708 A293325 * A251744 A251751 A251765

Adjacent sequences: A251710 A251711 A251712 * A251714 A251715 A251716

Keyword

nonn,easy

Author

Arie Bos, Dec 07 2014

Status

approved