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Search: id:A080528
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| A080528 |
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Sum of multinomials of (-1 +number of runs) in the partitions of n. |
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+0
1
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| 1, 2, 3, 5, 7, 12, 17, 28, 42, 68, 104, 171, 268, 442, 715, 1192, 1970, 3332, 5611, 9614, 16472, 28546, 49583, 86876, 152656, 269983, 479077, 854309, 1528314, 2745113, 4945015, 8937266
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OFFSET
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1,2
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COMMENT
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Sum of multinomials of number of runs in the partitions of n equals 2^(n-1), so a(n) is less than 2^(n-1).
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EXAMPLE
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The partitions of 4: {4},{3,1},{2,2},{2,1,1},{1,1,1,1} have {1},{1,1},{2},{2,1},{4} runs of equal integers. The sum of the Multinomials of {0},{0,0},{1},{1,0},{3} equals 5.
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MATHEMATICA
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multiplicity2[li:{__Integer}] := (Multinomial@@(-1+Length/@Split[ # ]))&[Sort@li]; Table[Plus@@multiplicity2/@Partitions[n], {n, 32}]
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CROSSREFS
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Sequence in context: A060730 A123569 A048816 this_sequence A002965 A091696 A048808
Adjacent sequences: A080525 A080526 A080527 this_sequence A080529 A080530 A080531
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KEYWORD
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easy,nonn
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AUTHOR
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Wouter Meeussen (wouter.meeussen(AT)pandora.be), Mar 22 2003
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