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Search: id:A143284
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| A143284 |
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Number of binary words of length n containing at least one subword 100001 and no subwords 10^{i}1 with i<4. |
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+0
2
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| 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 7, 11, 17, 25, 35, 48, 66, 92, 129, 180, 249, 342, 468, 640, 875, 1195, 1629, 2216, 3009, 4080, 5526, 7477, 10107, 13649, 18415, 24823, 33433, 44995, 60513, 81330, 109241, 146644, 196742, 263813, 353570, 473640, 634201
(list; graph; listen)
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OFFSET
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0,8
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FORMULA
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G.f.: x^6/((x^5+x-1)(x^6+x-1)). a(n)=(A003520(n+4)-A005708(n+5).
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EXAMPLE
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a(7)=2 because 2 binary words of length 7 have at least one subword 100001 and no subwords 10^{i}1 with i<4: 0100001, 1000010.
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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(4); seq (a(n), n=0..55);
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CROSSREFS
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Cf. A003520, A005708, 4th column of A143291.
Sequence in context: A108318 A006456 A018134 this_sequence A015856 A060437 A133428
Adjacent sequences: A143281 A143282 A143283 this_sequence A143285 A143286 A143287
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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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