A375404 Number of integer partitions of n whose minima of maximal anti-runs are not all different.

0, 0, 1, 1, 3, 3, 7, 9, 14, 19, 30, 38, 56, 73, 102, 133, 179, 231, 307, 392, 511, 647, 831, 1046, 1328, 1658, 2084, 2586, 3219, 3970, 4909, 6016, 7386, 9005, 10988, 13330, 16175, 19531, 23580, 28350, 34067, 40788, 48809, 58215, 69383, 82461, 97917, 115976

Offset: 0

Author

Gus Wiseman, Aug 17 2024

Keywords

• nonn

Comments

An anti-run is a sequence with no adjacent equal terms. The minima of maximal anti-runs in a sequence are obtained by splitting it into maximal anti-run subsequences and taking the least term of each.

Also the number of reversed integer partitions of n such that the minima of maximal anti-runs are not all different.

Examples

			The a(0) = 0 through a(8) = 14 reversed partitions:
  .  .  (11)  (111)  (22)    (113)    (33)      (115)      (44)
                     (112)   (1112)   (114)     (223)      (116)
                     (1111)  (11111)  (222)     (1114)     (224)
                                      (1113)    (1123)     (1115)
                                      (1122)    (1222)     (1124)
                                      (11112)   (11113)    (1133)
                                      (111111)  (11122)    (2222)
                                                (111112)   (11114)
                                                (1111111)  (11123)
                                                           (11222)
                                                           (111113)
                                                           (111122)
                                                           (1111112)
                                                           (11111111)
		

Crossrefs

The complement for maxima instead of minima is A375133, ranks A375402.

The complement is counted by A375134, ranks A375398.

These partitions are ranked by A375399.

For maxima instead of minima we have A375401, ranks A375403.

For identical instead of distinct we have A375405, ranks A375397.

A000041 counts integer partitions, strict A000009.

A003242 counts anti-run compositions, ranks A333489.

A055887 counts sequences of partitions with total sum n.

A375128 lists minima of maximal anti-runs of prime indices, sums A374706.

Cf. A034296, A046660, A073492, A115029, A141199, A239955, A279790, A358830, A358836, A375136.

Programs

Mathematica

Table[Length[Select[IntegerPartitions[n], !UnsameQ@@Min/@Split[#,UnsameQ]&]],{n,0,30}]