A325332 Number of totally abnormal integer partitions of n.

0, 0, 1, 1, 2, 1, 3, 1, 4, 2, 5, 1, 8, 1, 7, 5, 10, 2, 16, 4, 21, 15, 24, 17, 49, 29, 53, 53, 84, 65, 121, 92, 148, 141, 186, 179, 280, 223, 317, 318, 428, 387, 576, 512, 700, 734, 899, 900, 1260, 1207, 1551, 1668, 2041, 2109, 2748, 2795, 3463, 3775, 4446

Offset

0,5

Comments

A multiset is normal if its union is an initial interval of positive integers. A multiset is totally abnormal if it is not normal and either it is a singleton or its multiplicities form a totally abnormal multiset.

The Heinz numbers of these partitions are given by A325372.

Links

Table of n, a(n) for n=0..58.

Example

The a(2) = 1 through a(12) = 8 totally abnormal partitions (A = 10, B = 11, C = 12):
  (2)  (3)  (4)   (5)  (6)    (7)  (8)     (9)    (A)      (B)   (C)
            (22)       (33)        (44)    (333)  (55)           (66)
                       (222)       (2222)         (3322)         (444)
                                   (3311)         (4411)         (3333)
                                                  (22222)        (4422)
                                                                 (5511)
                                                                 (222222)
                                                                 (333111)

Mathematica

normQ[m_]:=Or[m=={}, Union[m]==Range[Max[m]]];
antinrmQ[ptn_]:=!normQ[ptn]&&(Length[ptn]==1||antinrmQ[Sort[Length/@Split[ptn]]]);
Table[Length[Select[IntegerPartitions[n], antinrmQ]], {n, 0, 30}]

Crossrefs

Cf. A181819, A275870, A305563, A317088, A317245, A317491, A317589, A319149, A319810, A325372.

Sequence in context: A064576 A322390 A113308 * A358195 A143862 A115118

Adjacent sequences: A325329 A325330 A325331 * A325333 A325334 A325335

Keyword

nonn

Author

Gus Wiseman, May 01 2019

Status

approved