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A143290
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Number of binary words of length n containing at least one subword 10^{10}1 and no subwords 10^{i}1 with i<10.
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1
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 17, 23, 31, 41, 53, 67, 83, 101, 121, 143, 168, 198, 236, 285, 348, 428, 528, 651, 800, 978, 1188, 1434, 1722, 2061, 2464, 2948, 3534, 4247, 5116, 6174, 7458, 9009, 10873, 13103, 15762, 18927
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OFFSET
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0,14
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LINKS
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Table of n, a(n) for n=0..59.
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FORMULA
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G.f.: x^12/((x^11+x-1)(x^12+x-1)). a(n)=A017905(n+21)-A017906(n+23).
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EXAMPLE
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a(13)=2 because 2 binary words of length 13 have at least one subword 10^{10}1 and no subwords 10^{i}1 with i<10: 0100000000001, 1000000000010.
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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(10); seq (a(n), n=0..66);
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CROSSREFS
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Cf. A017905, A017906, 10th column of A143291.
Sequence in context: A107062 A178538 A017904 * A044961 A044823 A048309
Adjacent sequences: A143287 A143288 A143289 * A143291 A143292 A143293
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz, Aug 04 2008
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STATUS
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approved
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