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A143289
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Number of binary words of length n containing at least one subword 10^{9}1 and no subwords 10^{i}1 with i<9.
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1
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 16, 22, 30, 40, 52, 66, 82, 100, 120, 143, 171, 207, 254, 315, 393, 491, 612, 759, 935, 1144, 1392, 1688, 2045, 2480, 3014, 3672, 4483, 5480, 6700, 8185, 9984, 12156, 14774, 17930, 21740, 26349, 31936
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,13
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FORMULA
| G.f.: x^11/((x^10+x-1)(x^11+x-1)). a(n)=A017904(n+19)-A017905(n+21).
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EXAMPLE
| a(12)=2 because 2 binary words of length 12 have at least one subword 10^{9}1 and no subwords 10^{i}1 with i<9: 010000000001, 100000000010.
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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(9); seq (a(n), n=0..65);
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CROSSREFS
| Cf. A017904, A017905, 9th column of A143291.
Sequence in context: A059765 A180479 A193456 * A064807 A007603 A005349
Adjacent sequences: A143286 A143287 A143288 * A143290 A143291 A143292
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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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