A325193 Number of integer partitions whose sum plus co-rank is n, where co-rank is maximum of length and largest part.

1, 0, 1, 0, 2, 1, 3, 2, 5, 5, 8, 8, 14, 14, 22, 24, 35, 39, 54, 62, 84, 97, 127, 148, 192, 224, 284, 334, 418, 492, 610, 716, 880, 1035, 1259, 1480, 1790, 2100, 2522, 2958, 3533, 4135, 4916, 5742, 6798, 7928, 9344, 10878, 12778, 14846, 17378, 20156, 23520

Offset

0,5

Links

Table of n, a(n) for n=0..52.

FindStat, St000784: The maximum of the length and the largest part of the integer partition

Example

The a(4) = 2 through a(12) = 14 partitions:
  (2)   (21)  (3)    (31)   (4)     (33)    (5)      (43)     (6)
  (11)        (22)   (211)  (32)    (41)    (42)     (51)     (44)
              (111)         (221)   (222)   (322)    (332)    (52)
                            (311)   (321)   (331)    (421)    (333)
                            (1111)  (2111)  (411)    (2221)   (422)
                                            (2211)   (3211)   (431)
                                            (3111)   (4111)   (511)
                                            (11111)  (21111)  (2222)
                                                              (3221)
                                                              (3311)
                                                              (4211)
                                                              (22111)
                                                              (31111)
                                                              (111111)

Mathematica

Table[Sum[Length[Select[IntegerPartitions[k], Max[Length[#], Max[#]]==n-k&]], {k, 0, n}], {n, 0, 30}]

Crossrefs

Row sums of A325194.

Cf. A051924, A065770, A071724, A096771, A115720, A252464, A257990, A263297, A325178, A325189, A325192.

Sequence in context: A128100 A035579 A045931 * A079974 A102517 A062951

Adjacent sequences: A325190 A325191 A325192 * A325194 A325195 A325196

Keyword

nonn

Author

Gus Wiseman, Apr 12 2019

Status

approved