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Search: id:A143286
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| A143286 |
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Number of binary words of length n containing at least one subword 10^{6}1 and no subwords 10^{i}1 with i<6. |
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+0
2
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| 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 9, 13, 19, 27, 37, 49, 63, 80, 102, 132, 173, 228, 300, 392, 508, 654, 839, 1076, 1382, 1778, 2289, 2945, 3783, 4850, 6207, 7934, 10135, 12943, 16526, 21095, 26915, 34320, 43733, 55692, 70882, 90174, 114673, 145778
(list; graph; listen)
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OFFSET
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0,10
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FORMULA
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G.f.: x^8/((x^7+x-1)(x^8+x-1)). a(n)=A005709(n+6)-A005710(n+7).
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EXAMPLE
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a(9)=2 because 2 binary words of length 9 have at least one subword 10^{6}1 and no subwords 10^{i}1 with i<6: 010000001, 100000010.
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MAPLE
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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(6); seq (a(n), n=0..60);
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CROSSREFS
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Cf. A005709, A005710, 6th column of A143291.
Sequence in context: A017900 A005708 A085793 this_sequence A160339 A033072 A030287
Adjacent sequences: A143283 A143284 A143285 this_sequence A143287 A143288 A143289
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 04 2008
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