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Search: id:A097091
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| A097091 |
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Number of partitions of n such that the least part occurs exactly three times. |
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+0
5
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| 0, 0, 1, 0, 1, 2, 2, 2, 6, 5, 8, 11, 15, 18, 27, 30, 43, 54, 69, 83, 113, 134, 172, 211, 265, 320, 405, 483, 602, 726, 888, 1064, 1306, 1554, 1884, 2248, 2707, 3213, 3860, 4560, 5446, 6435, 7638, 8990, 10651, 12494, 14734, 17260, 20277, 23683, 27754, 32328
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OFFSET
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1,6
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FORMULA
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G.f.: Sum_{m>0} (x^(3*m) / Product_{i>m} (1-x^i)). More generally, g.f. for number of partitions of n such that the least part occurs exactly k times is Sum_{m>0} (x^(k*m) / Product_{i>m} (1-x^i)). Vladeta Jovovic (vladeta(AT)eunet.rs)
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MATHEMATICA
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(* do first *) Needs["DiscreteMath`Combinatorica`"] (* then *) f[n_] := Block[{p = Partitions[n], l = PartitionsP[n], c = 0, k = 1}, While[k < l + 1, q = PadLeft[ p[[k]], 4]; If[ q[[1]] != q[[4]] && q[[2]] == q[[4]], c++ ]; k++ ]; c]; Table[ f[n], {n, 52}]
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CROSSREFS
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Cf. A002865, A096373, A097093, A097093.
Sequence in context: A038074 A059885 A145890 this_sequence A094204 A088681 A078584
Adjacent sequences: A097088 A097089 A097090 this_sequence A097092 A097093 A097094
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 24 2004
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