%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