login
7-step Fibonacci sequence starting with (0,0,1,0,0,0,0).
4

%I #13 Jun 13 2015 00:55:18

%S 0,0,1,0,0,0,0,1,2,4,7,14,28,56,112,223,444,884,1761,3508,6988,13920,

%T 27728,55233,110022,219160,436559,869610,1732232,3450544,6873360,

%U 13691487,27272952,54326744,108216929,215564248,429396264,855341984,1703810608,3393929729

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

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,1,1,1,1).

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

%t LinearRecurrence[Table[1, {7}], {0, 0, 1, 0, 0, 0, 0}, 40] (* _Michael De Vlieger_, Dec 09 2014 *)

%o (J) (see www.jsoftware.com) First construct the generating matrix

%o [M=: (#.@}: + {:)\"1&.|: <:/~i.7

%o 1 1 1 1 1 1 1

%o 1 2 2 2 2 2 2

%o 2 3 4 4 4 4 4

%o 4 6 7 8 8 8 8

%o 8 12 14 15 16 16 16

%o 16 24 28 30 31 32 32

%o 32 48 56 60 62 63 64

%o Given that matrix, one can produce the first 7*150 numbers by

%o , M(+/ . *)^:(i.150) 0 0 1 0 0 0 0x

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

%K nonn,easy

%O 0,9

%A _Arie Bos_, Dec 07 2014