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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.
5
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, 130, 194, 232, 230, 187, 132, 129, 218, 364, 497, 576, 578, 498, 367, 290, 378, 642, 977, 1264, 1435, 1448, 1290, 1000, 735, 728
OFFSET
0,4
COMMENTS
The Heinz numbers of these partitions are given by A325197.
EXAMPLE
The a(3) = 2 through a(10) = 15 partitions (empty columns not shown):
(3) (41) (33) (43) (521) (333) (433)
(111) (2111) (42) (2221) (32111) (441) (442)
(222) (4111) (522) (532)
(411) (531) (541)
(2211) (3222) (3322)
(3111) (5211) (3331)
(32211) (4222)
(33111) (4411)
(42111) (5221)
(5311)
(32221)
(33211)
(42211)
(43111)
(52111)
MATHEMATICA
otb[ptn_]:=Min@@MapIndexed[#1+#2[[1]]-1&, Append[ptn, 0]];
otbmax[ptn_]:=Max@@MapIndexed[#1+#2[[1]]-1&, Append[ptn, 0]];
Table[Length[Select[IntegerPartitions[n], otbmax[#]-otb[#]==2&]], {n, 0, 30}]
KEYWORD
nonn,look
AUTHOR
Gus Wiseman, Apr 11 2019
STATUS
approved