Search: id:A143289
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%I A143289
%S A143289 0,0,0,0,0,0,0,0,0,0,0,1,2,3,4,5,6,7,8,9,10,12,16,22,30,40,52,66,82,100,
%T A143289 120,143,171,207,254,315,393,491,612,759,935,1144,1392,1688,2045,2480,
%U A143289 3014,3672,4483,5480,6700,8185,9984,12156,14774,17930,21740,26349,31936
%N A143289 Number of binary words of length n containing at least one subword 10^{9}1 
               and no subwords 10^{i}1 with i<9.
%F A143289 G.f.: x^11/((x^10+x-1)(x^11+x-1)). a(n)=A017904(n+19)-A017905(n+21).
%e A143289 a(12)=2 because 2 binary words of length 12 have at least one subword 
               10^{9}1 and no subwords 10^{i}1 with i<9: 010000000001, 100000000010.
%p A143289 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(9); seq (a(n), n=0..65);
%Y A143289 Cf. A017904, A017905, 9th column of A143291.
%Y A143289 Sequence in context: A017903 A005711 A059765 this_sequence A064807 A007603 
               A005349
%Y A143289 Adjacent sequences: A143286 A143287 A143288 this_sequence A143290 A143291 
               A143292
%K A143289 nonn
%O A143289 0,13
%A A143289 Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 04 2008

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