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 A325182 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 2. 5
 0, 0, 0, 2, 2, 1, 2, 4, 7, 6, 5, 4, 5, 9, 12, 15, 14, 12, 10, 9, 11, 15, 21, 24, 28, 26, 24, 20, 18, 17, 19, 25, 31, 38, 42, 46, 44, 41, 36, 32, 29, 28, 31, 37, 46, 53, 62, 66, 71, 68, 65, 58, 53, 47, 44, 43, 46, 54, 63, 74, 83, 93, 98, 103, 100, 96, 88, 81 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 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. REFERENCES Richard P. Stanley, Enumerative Combinatorics, Volume 2,  Cambridge University Press, 1999, p. 289. LINKS Wikipedia, Durfee square. EXAMPLE The a(3) = 2 through a(14) = 12 partitions:   3    31   311  42    43    44    432   442   533    543    544    554   111  211       2211  421   422   441   3322  4322   4422   553    5333                        2221  431   3222  4222  4421   5331   5332   5432                        3211  2222  3321  4321  33311  33321  5431   5441                              3221  4221  4411         43311  33322  5531                              3311  4311                      33331  33332                              4211                            43321  43322                                                              44311  43331                                                              53311  44321                                                                     44411                                                                     53321                                                                     54311 MATHEMATICA durf[ptn_]:=Length[Select[Range[Length[ptn]], ptn[[#]]>=#&]]; codurf[ptn_]:=Max[Length[ptn], Max[ptn]]; Table[Length[Select[IntegerPartitions[n], codurf[#]-durf[#]==2&]], {n, 0, 30}] CROSSREFS Cf. A006918, A096771, A257990, A263297, A325168. Cf. A325178, A325180, A325181, A325182, A325192, A325197, A325199, A325200. Sequence in context: A230290 A294783 A172021 * A215959 A209555 A059594 Adjacent sequences:  A325179 A325180 A325181 * A325183 A325184 A325185 KEYWORD nonn,look AUTHOR Gus Wiseman, Apr 08 2019 STATUS approved

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Last modified December 1 11:30 EST 2021. Contains 349429 sequences. (Running on oeis4.)