cp's OEIS Frontend

A325199 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.

%I A325199 #14 Apr 23 2019 11:14:48
%S A325199 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 A325199 130,194,232,230,187,132,129,218,364,497,576,578,498,367,290,378,642,
%U A325199 977,1264,1435,1448,1290,1000,735,728
%N A325199 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 A325199 The Heinz numbers of these partitions are given by A325197.
%H A325199 FindStat, <a href="http://www.findstat.org/StatisticsDatabase/St000384">St000384: The maximal part of the shifted composition of an integer partition</a>
%H A325199 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 A325199 The a(3) = 2 through a(10) = 15 partitions (empty columns not shown):
%e A325199   (3)    (41)    (33)    (43)    (521)    (333)    (433)
%e A325199   (111)  (2111)  (42)    (2221)  (32111)  (441)    (442)
%e A325199                  (222)   (4111)           (522)    (532)
%e A325199                  (411)                    (531)    (541)
%e A325199                  (2211)                   (3222)   (3322)
%e A325199                  (3111)                   (5211)   (3331)
%e A325199                                           (32211)  (4222)
%e A325199                                           (33111)  (4411)
%e A325199                                           (42111)  (5221)
%e A325199                                                    (5311)
%e A325199                                                    (32221)
%e A325199                                                    (33211)
%e A325199                                                    (42211)
%e A325199                                                    (43111)
%e A325199                                                    (52111)
%t A325199 otb[ptn_]:=Min@@MapIndexed[#1+#2[[1]]-1&,Append[ptn,0]];
%t A325199 otbmax[ptn_]:=Max@@MapIndexed[#1+#2[[1]]-1&,Append[ptn,0]];
%t A325199 Table[Length[Select[IntegerPartitions[n],otbmax[#]-otb[#]==2&]],{n,0,30}]
%Y A325199 Column k=2 of A325200.
%Y A325199 Cf. A046660, A065770, A071724, A243055, A325166, A325169, A325178, A325188, A325189, A325191, A325195, A325197, A325198.
%K A325199 nonn,look
%O A325199 0,4
%A A325199 _Gus Wiseman_, Apr 11 2019