cp's OEIS Frontend

A143283 Number of binary words of length n containing at least one subword 10001 and no subwords 10^{i}1 with i<3.

%I A143283 #6 Oct 01 2012 21:19:39
%S A143283 0,0,0,0,0,1,2,3,4,6,10,16,24,35,51,75,110,160,231,332,476,681,972,
%T A143283 1384,1966,2787,3944,5573,7864,11082,15597,21926,30791,43199,60553,
%U A143283 84807,118682,165966,231930,323905,452083,630629,879224,1225205,1706532,2375901
%N A143283 Number of binary words of length n containing at least one subword 10001 and no subwords 10^{i}1 with i<3.
%H A143283 Alois P. Heinz, <a href="/A143283/b143283.txt">Table of n, a(n) for n = 0..1000</a>
%F A143283 G.f.: x^5/((x^4+x-1)*(x^5+x-1)).
%F A143283 a(n) = A003269(n+4) - A003520(n+4).
%e A143283 a(9) = 6 because 6 binary words of length 8 have at least one subword 10001 and no subwords 11, 101 or 1001: 000010001, 000100010, 001000100, 010001000, 100010000, 100010001.
%p A143283 a:= proc(m) local M;
%p A143283       M:= Matrix (2*m+3, (i, j)-> `if` (i=j-1 and i<>m+1 or j=1 and
%p A143283                   i in [1, m+1] or j=m+2 and i in [m+2, 2*m+3], 1, 0));
%p A143283       proc(n) local K; K:= M^(n+m+1); K[m+1, 1] -K[m+2, m+2] end
%p A143283     end(3):
%p A143283 seq (a(n), n=0..55);
%Y A143283 Cf. A003269, A003520, 3rd column of A143291.
%K A143283 nonn
%O A143283 0,7
%A A143283 _Alois P. Heinz_, Aug 04 2008