%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