%I A143281
%S A143281 0,0,0,1,2,4,8,15,27,48,84,145,248,421,710,1191,1989,3309,5487,9073,
%T A143281 14966,24634,40472,66384,108729,177858,290610,474364,773615,1260643,
%U A143281 2052818,3340662,5433345,8832432,14351403,23309326,37844645,61423513
%N A143281 Number of binary words of length n containing at least one subword 101 
               and no subword 11.
%F A143281 G.f.: x^3/((x^2+x-1)(x^3+x-1)). a(n)=A000045(n+2)-A000930(n+2).
%e A143281 a(6)=8 because 8 binary words of length 6 have at least one substring 
               101 and no substring 11: 000101, 001010, 010100, 101000, 010101, 
               101010, 101001, 100101.
%p A143281 a := proc (m) option remember; local M; M := Matrix (2*m+3, (i,j)-> if 
               m=0 and i=1 and j=1 then 2 elif (i=j-1 and i <> m+1) or (j=1 and 
               member (i,[1,m+1])) or (j=m+2 and member(i,[m+2,2*m+3])) then 1 else 
               0 fi); if m=0 then RETURN (proc(n) local K; K := M^(n+m+1); K[m+1,
               1]/2-K[m+2,m+2] end) else RETURN (proc(n) local K; K := M^(n+m+1); 
               K[m+1,1]-K[m+2,m+2] end) fi end(1); seq (a(n), n=0..50);
%Y A143281 Cf. A000045, A000930, 1st column of A143291.
%Y A143281 Sequence in context: A054174 A001523 A000126 this_sequence A098057 A074029 
               A138653
%Y A143281 Adjacent sequences: A143278 A143279 A143280 this_sequence A143282 A143283 
               A143284
%K A143281 nonn
%O A143281 0,5
%A A143281 Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 04 2008