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A143288
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Number of binary words of length n containing at least one subword 10^{8}1 and no subwords 10^{i}1 with i<8.
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1
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 15, 21, 29, 39, 51, 65, 81, 99, 120, 146, 180, 225, 284, 360, 456, 575, 720, 895, 1106, 1362, 1676, 2065, 2550, 3156, 3912, 4851, 6011, 7437, 9184, 11321, 13936, 17141, 21077, 25919, 31881, 39222, 48254
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,12
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FORMULA
| G.f.: x^10/((x^9+x-1)(x^10+x-1)). a(n)=A005711(n+7)-A017904(n+19).
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EXAMPLE
| a(11)=2 because 2 binary words of length 11 have at least one subword 10^{8}1 and no subwords 10^{i}1 with i<8: 01000000001, 10000000010.
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MAPLE
| 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(8); seq (a(n), n=0..63);
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CROSSREFS
| Cf. A005711, A017904, 8th column of A143291.
Sequence in context: A050761 A030721 A190296 * A001103 A084034 A147591
Adjacent sequences: A143285 A143286 A143287 * A143289 A143290 A143291
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KEYWORD
| nonn
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AUTHOR
| Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 04 2008
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