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Search: id:A119407
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| A119407 |
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Number of nonempty subsets of {1,2,...,n} with no gap of length greater than 4 (a set S has a gap of length d if a and b are in S but no x with a<x<b is in S, where b-a=d). |
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1
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| 1, 3, 7, 15, 31, 62, 122, 238, 462, 894, 1727, 3333, 6429, 12397, 23901, 46076, 88820, 171212, 330028, 636156, 1226237, 2363655, 4556099, 8782171
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OFFSET
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1,2
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COMMENT
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The numbers of subsets of {1,2,...,n} with no gap of length greater than d, for d=1,2 and 3, seem to be given in A000217, A001924 and A062544, respectively.
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FORMULA
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G.f. for number of nonempty subsets of {1,2,...,n} with no gap of length greater than d is x/((1-x)*(1-2*x+x^(d+1))). - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 27 2008
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CROSSREFS
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Cf. A000217, A001924, A062544.
Sequence in context: A034480 A057703 A006739 this_sequence A043734 A151359 A147596
Adjacent sequences: A119404 A119405 A119406 this_sequence A119408 A119409 A119410
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KEYWORD
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nonn
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AUTHOR
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John W. Layman (layman(AT)math.vt.edu), Jul 25 2006
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