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Search: id:A097093
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| A097093 |
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Number of partitions of n such that the least part occurs exactly five times. |
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+0
5
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| 0, 0, 0, 0, 1, 0, 1, 1, 2, 3, 4, 4, 8, 9, 14, 16, 23, 27, 39, 48, 62, 76, 100, 120, 159, 190, 241, 292, 367, 443, 552, 663, 816, 980, 1200, 1430, 1742, 2075, 2504, 2979, 3575, 4232, 5063, 5980, 7114, 8382, 9930, 11663, 13773, 16140, 18980, 22190, 26017
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OFFSET
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1,9
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FORMULA
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G.f.: Sum_{m>0} (x^(5*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.yu)
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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]], 6]; If[ q[[1]] != q[[6]] && q[[2]] == q[[6]], c++ ]; k++ ]; c]; Table[ f[n], {n, 54}]
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CROSSREFS
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Cf. A002865, A096373, A097091, A097092.
Sequence in context: A136330 A028298 A047966 this_sequence A056877 A118263 A102539
Adjacent sequences: A097090 A097091 A097092 this_sequence A097094 A097095 A097096
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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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