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Search: id:A143282
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| A143282 |
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Number of binary words of length n containing at least one subword 1001 and no subwords 10^{i}1 with i<2. |
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+0
2
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| 0, 0, 0, 0, 1, 2, 3, 5, 9, 15, 24, 38, 60, 94, 146, 225, 345, 527, 802, 1216, 1838, 2771, 4168, 6256, 9372, 14016, 20929, 31208, 46476, 69133, 102726, 152494, 226171, 335169, 496320, 734440, 1086102, 1605187, 2371049, 3500522, 5165573, 7619251
(list; graph; listen)
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OFFSET
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0,6
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FORMULA
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G.f.: x^4/((x^3+x-1)(x^4+x-1)). a(n)=A000930(n+2)-A003269(n+4).
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EXAMPLE
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a(7)=5 because 5 binary words of length 7 have at least one subword 1001 and no subwords 11 or 101: 0001001, 0010010, 0100100, 1001000, 1001001.
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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(2); seq (a(n), n=0..50);
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CROSSREFS
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Cf. A000930, A003269, 2nd column of A143291.
Sequence in context: A067798 A074693 A147322 this_sequence A097083 A147877 A003476
Adjacent sequences: A143279 A143280 A143281 this_sequence A143283 A143284 A143285
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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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