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%I #14 Apr 23 2019 11:14:48
%S 0,0,0,2,0,2,6,3,2,9,15,12,6,12,27,38,34,22,20,43,74,94,90,67,48,69,
%T 130,194,232,230,187,132,129,218,364,497,576,578,498,367,290,378,642,
%U 977,1264,1435,1448,1290,1000,735,728
%N Number of integer partitions of n such that the difference between the length of the minimal triangular partition containing and the maximal triangular partition contained in the Young diagram is 2.
%C The Heinz numbers of these partitions are given by A325197.
%H FindStat, <a href="http://www.findstat.org/StatisticsDatabase/St000384">St000384: The maximal part of the shifted composition of an integer partition</a>
%H FindStat, <a href="http://www.findstat.org/StatisticsDatabase/St000783">St000783: The maximal number of occurrences of a colour in a proper colouring of a Ferrers diagram</a>
%e The a(3) = 2 through a(10) = 15 partitions (empty columns not shown):
%e (3) (41) (33) (43) (521) (333) (433)
%e (111) (2111) (42) (2221) (32111) (441) (442)
%e (222) (4111) (522) (532)
%e (411) (531) (541)
%e (2211) (3222) (3322)
%e (3111) (5211) (3331)
%e (32211) (4222)
%e (33111) (4411)
%e (42111) (5221)
%e (5311)
%e (32221)
%e (33211)
%e (42211)
%e (43111)
%e (52111)
%t otb[ptn_]:=Min@@MapIndexed[#1+#2[[1]]-1&,Append[ptn,0]];
%t otbmax[ptn_]:=Max@@MapIndexed[#1+#2[[1]]-1&,Append[ptn,0]];
%t Table[Length[Select[IntegerPartitions[n],otbmax[#]-otb[#]==2&]],{n,0,30}]
%Y Column k=2 of A325200.
%Y Cf. A046660, A065770, A071724, A243055, A325166, A325169, A325178, A325188, A325189, A325191, A325195, A325197, A325198.
%K nonn,look
%O 0,4
%A _Gus Wiseman_, Apr 11 2019
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