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Search: id:A143283
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| A143283 |
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Number of binary words of length n containing at least one subword 10001 and no subwords 10^{i}1 with i<3. |
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+0
2
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| 0, 0, 0, 0, 0, 1, 2, 3, 4, 6, 10, 16, 24, 35, 51, 75, 110, 160, 231, 332, 476, 681, 972, 1384, 1966, 2787, 3944, 5573, 7864, 11082, 15597, 21926, 30791, 43199, 60553, 84807, 118682, 165966, 231930, 323905, 452083, 630629, 879224, 1225205, 1706532
(list; graph; listen)
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OFFSET
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0,7
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FORMULA
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G.f.: x^5/((x^4+x-1)(x^5+x-1)). a(n)=A003269(n+4)-A003520(n+4).
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EXAMPLE
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a(9)=6 because 6 binary words of length 8 have at least one subword 10001 and no subwords 11, 101 or 1001: 000010001, 000100010, 001000100, 010001000, 100010000, 100010001.
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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(3); seq (a(n), n=0..55);
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CROSSREFS
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Cf. A003269, A003520, 3rd column of A143291.
Sequence in context: A018062 A070542 A098855 this_sequence A104767 A072944 A024722
Adjacent sequences: A143280 A143281 A143282 this_sequence A143284 A143285 A143286
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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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