

A097092


Number of partitions of n such that the least part occurs exactly four times.


4



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
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OFFSET

1,8


COMMENTS

Number of partitions p of n such that 3*min(p) + (number of parts of p) is a part of p.  Clark Kimberling, Feb 28 2014


LINKS

Table of n, a(n) for n=1..53.


FORMULA

G.f.: Sum_{m>0} (x^(4*m) / Product_{i>m} (1x^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} (1x^i)). Vladeta Jovovic


MATHEMATICA

a[n_] := Module[{p = IntegerPartitions[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[ a[n], {n, 53}]
Table[Count[IntegerPartitions[n], p_ /; MemberQ[p, Length[p] + 3*Min[p]]], {n, 50}] (* Clark Kimberling, Feb 28 2014 *)


CROSSREFS

Cf. A002865, A096373, A097091, A097093.
Sequence in context: A001612 A275901 A305369 * A241417 A211363 A059320
Adjacent sequences: A097089 A097090 A097091 * A097093 A097094 A097095


KEYWORD

nonn


AUTHOR

Robert G. Wilson v, Jul 24 2004


STATUS

approved



