cp's OEIS Frontend

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

%I A251713 #15 Mar 28 2025 10:33:31
%S A251713 0,0,1,0,0,0,0,1,2,4,7,14,28,56,112,223,444,884,1761,3508,6988,13920,
%T A251713 27728,55233,110022,219160,436559,869610,1732232,3450544,6873360,
%U A251713 13691487,27272952,54326744,108216929,215564248,429396264,855341984,1703810608,3393929729
%N A251713 7-step Fibonacci sequence starting with (0,0,1,0,0,0,0).
%H A251713 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,1,1,1,1).
%F A251713 a(n+7) = a(n) + a(n+1) + a(n+2) + a(n+3) + a(n+4) + a(n+5) + a(n+6).
%F A251713 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
%t A251713 LinearRecurrence[Table[1, {7}], {0, 0, 1, 0, 0, 0, 0}, 40] (* _Michael De Vlieger_, Dec 09 2014 *)
%o A251713 (J) (see www.jsoftware.com) First construct the generating matrix
%o A251713    [M=: (#.@}: + {:)\"1&.|: <:/~i.7
%o A251713  1  1  1  1  1  1  1
%o A251713  1  2  2  2  2  2  2
%o A251713  2  3  4  4  4  4  4
%o A251713  4  6  7  8  8  8  8
%o A251713  8 12 14 15 16 16 16
%o A251713 16 24 28 30 31 32 32
%o A251713 32 48 56 60 62 63 64
%o A251713 Given that matrix, one can produce the first 7*150 numbers by
%o A251713 , M(+/ . *)^:(i.150) 0 0 1 0 0 0 0x
%Y A251713 Other 7-step Fibonacci sequences are A066178, A104621, A122189, A251710, A251711, A251712, A251714.
%K A251713 nonn,easy
%O A251713 0,9
%A A251713 _Arie Bos_, Dec 07 2014