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Search: id:A097092
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| A097092 |
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Number of partitions of n such that the least part occurs exactly four times. |
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+0
4
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| 0, 0, 0, 1, 0, 1, 1, 3, 2, 4, 5, 9, 9, 14, 16, 26, 29, 40, 48, 67, 79, 105, 126, 165, 196, 253, 303, 385, 459, 572, 687, 852, 1014, 1244, 1482, 1807, 2145, 2595, 3075, 3701, 4375, 5231, 6170, 7350, 8641, 10247, 12025, 14201, 16620, 19557, 22839, 26790, 31209
(list; graph; listen)
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OFFSET
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1,8
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FORMULA
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G.f.: Sum_{m>0} (x^(4*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]], 5]; If[ q[[1]] != q[[5]] && q[[2]] == q[[5]], c++ ]; k++ ]; c]; Table[ f[n], {n, 53}]
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CROSSREFS
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Cf. A002865, A096373, A097091, A097093.
Sequence in context: A164287 A086962 A001612 this_sequence A059320 A129601 A049831
Adjacent sequences: A097089 A097090 A097091 this_sequence A097093 A097094 A097095
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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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