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Number of integer partitions of n such that the lesser of the maximum part and the number of parts is 3.
2

%I #4 Apr 13 2019 08:11:36

%S 0,0,0,0,1,3,6,9,13,16,20,24,28,32,38,42,48,54,60,66,74,80,88,96,104,

%T 112,122,130,140,150,160,170,182,192,204,216,228,240,254,266,280,294,

%U 308,322,338,352,368,384,400,416,434,450,468,486,504,522,542,560

%N Number of integer partitions of n such that the lesser of the maximum part and the number of parts is 3.

%e The a(5) = 1 through a(10) = 16 partitions:

%e (311) (321) (322) (332) (333) (433)

%e (411) (331) (422) (432) (442)

%e (3111) (421) (431) (441) (532)

%e (511) (521) (522) (541)

%e (3211) (611) (531) (622)

%e (31111) (3221) (621) (631)

%e (3311) (711) (721)

%e (32111) (3222) (811)

%e (311111) (3321) (3322)

%e (32211) (3331)

%e (33111) (32221)

%e (321111) (33211)

%e (3111111) (322111)

%e (331111)

%e (3211111)

%e (31111111)

%t Table[Length[Select[IntegerPartitions[n],Min[Length[#],Max[#]]==3&]],{n,30}]

%Y Column k = 3 of A325227.

%Y Cf. A051924, A096771, A115720, A265283, A325224, A325225, A325229, A325231, A325232.

%K nonn

%O 1,6

%A _Gus Wiseman_, Apr 12 2019