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A325181
Number of integer partitions of n such that the difference between the length of the minimal square containing and the maximal square contained in the Young diagram is 1.
6
0, 0, 2, 1, 0, 2, 3, 2, 1, 0, 2, 3, 4, 3, 2, 1, 0, 2, 3, 4, 5, 4, 3, 2, 1, 0, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 0, 2, 3, 4, 5, 6, 7, 6, 5, 4, 3, 2, 1, 0, 2, 3, 4, 5, 6, 7, 8, 7, 6, 5, 4, 3, 2, 1, 0, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 2, 3, 4, 5, 6
OFFSET
0,3
COMMENTS
The maximal square contained in the Young diagram of an integer partition is called its Durfee square, and its length is the rank of the partition.
LINKS
EXAMPLE
The a(2) = 2 through a(15) = 1 partitions:
(2) (21) (32) (33) (322) (332) (433) (443) (444) (4333) (4433) (4443)
(11) (221) (222) (331) (3331) (3332) (3333) (4432) (4442)
(321) (4331) (4332) (4441)
(4431)
MATHEMATICA
durf[ptn_]:=Length[Select[Range[Length[ptn]], ptn[[#]]>=#&]];
codurf[ptn_]:=Max[Length[ptn], Max[ptn]];
Table[Length[Select[IntegerPartitions[n], codurf[#]-durf[#]==1&]], {n, 0, 30}]
KEYWORD
nonn,look
AUTHOR
Gus Wiseman, Apr 08 2019
EXTENSIONS
More terms from Giovanni Resta, Apr 15 2019
STATUS
approved