A363262 Number of integer compositions of n in which the greatest part appears more than once.

0, 1, 1, 2, 4, 9, 18, 37, 73, 145, 287, 570, 1134, 2264, 4526, 9061, 18152, 36374, 72884, 146011, 292416, 585422, 1171632, 2344136, 4688821, 9376832, 18749169, 37485358, 74939850, 149813328, 299492966, 598729533, 1196987066, 2393137399, 4784846896, 9567357951

Offset: 1

Author

Gus Wiseman, Jun 04 2023

Keywords

• nonn

Comments

Also the number of multisets of length n covering an initial interval of positive integers with more than one mode.

Examples

			The a(2) = 1 through a(6) = 9 compositions:
  (11)  (111)  (22)    (122)    (33)
               (1111)  (212)    (222)
                       (221)    (1122)
                       (11111)  (1212)
                                (1221)
                                (2112)
                                (2121)
                                (2211)
                                (111111)
		

Crossrefs

For partitions instead of compositions we have A002865.

The complement is counted by A097979 shifted left.

Row sums of columns k > 1 of A238341.

If all parts appear more than once we have A240085, for partitions A007690.

If the greatest part appears exactly twice we have A243737.

For least instead of greatest we have A363224, see triangle A238342.

A000041 counts integer partitions, strict A000009.

A032020 counts strict compositions.

A067029 gives last exponent in prime factorization, first A071178.

A261982 counts compositions with some part appearing more than once.

Cf. A008284, A105039, A117989, A362607, A362608, A362612, A362614.

Programs

Mathematica

Table[Length[Select[Join@@Permutations /@ IntegerPartitions[n],Count[#,Max@@#]>1&]],{n,15}]