A198254 Number of maximum-diversity partitions of n.

1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 3, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset

0,3

Comments

A maximum-diversity partition of n is an integer partition whose part distribution maximizes the number of different compositions (=distinct partition orderings) that can be constructed from it.

An integer composition of n corresponds to a subgroup of the symmetric group on n element whose cycles are formed of contiguous integers.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Example

For n=17, there are 3 partitions reaching the maximum possible of 7!/2 =2520 distinct orderings : {4, 3, 2, 2, 2, 1, 1, 1, 1}, {4, 3, 2, 2, 1, 1, 1, 1, 1, 1} and {3, 3, 2, 2, 2, 1, 1, 1, 1, 1}.

Crossrefs

A102462 gives the number of compositions that can be constructed from a maximum-diversity partition of n.

Cf. A007294, A072811, A080575.

Sequence in context: A341998 A083894 A128257 * A309059 A368712 A293630

Adjacent sequences: A198251 A198252 A198253 * A198255 A198256 A198257

Keyword

nonn,nice

Author

Olivier Gérard, Oct 22 2011

Status

approved