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Search: id:A143287
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| A143287 |
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Number of binary words of length n containing at least one subword 10^{7}1 and no subwords 10^{i}1 with i<7. |
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+0
2
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| 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 14, 20, 28, 38, 50, 64, 80, 99, 123, 155, 198, 255, 329, 423, 540, 684, 861, 1080, 1354, 1700, 2139, 2696, 3400, 4285, 5392, 6772, 8490, 10630, 13300, 16637, 20812, 26036, 32568, 40726, 50902, 63582, 79372
(list; graph; listen)
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OFFSET
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0,11
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FORMULA
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G.f.: x^9/((x^8+x-1)(x^9+x-1)). a(n)=A005710(n+7)-A005711(n+7).
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EXAMPLE
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a(10)=2 because 2 binary words of length 10 have at least one subword 10^{7}1 and no subwords 10^{i}1 with i<7: 0100000001, 1000000010.
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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(7); seq (a(n), n=0..62);
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CROSSREFS
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Cf. A005710, A005711, 7th column of A143291.
Sequence in context: A005709 A101917 A127273 this_sequence A033073 A039172 A044958
Adjacent sequences: A143284 A143285 A143286 this_sequence A143288 A143289 A143290
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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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