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 A198254 Number of maximum-diversity partitions of n. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 17 05:28 EDT 2024. Contains 375985 sequences. (Running on oeis4.)