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A304648 Number of different periodic multisets that fit within some normal multiset of weight n. 0
0, 1, 3, 7, 13, 25, 44, 78, 136, 242, 422, 747, 1314 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

A multiset is normal if it spans an initial interval of positive integers. It is periodic if its multiplicities have a common divisor greater than 1.

LINKS

Table of n, a(n) for n=1..13.

EXAMPLE

The a(5) = 13 periodic multisets:

(11), (22), (33), (44),

(111), (222), (333),

(1111), (1122), (1133), (2222), (2233),

(11111).

MATHEMATICA

allnorm[n_Integer]:=Function[s, Array[Count[s, y_/; y<=#]+1&, n]]/@Subsets[Range[n-1]+1];

Table[Length[Select[Union@@Rest/@Subsets/@allnorm[n], GCD@@Length/@Split[#]>1&]], {n, 10}]

CROSSREFS

Cf. A000217, A001597, A018783, A027941, A178472, A210554, A303547, A303709, A303974, A303976.

Sequence in context: A092463 A259343 A210613 * A243737 A269832 A201081

Adjacent sequences:  A304645 A304646 A304647 * A304649 A304650 A304651

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, May 15 2018

EXTENSIONS

a(12)-a(13) from Robert Price, Sep 15 2018

STATUS

approved

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Last modified October 14 00:05 EDT 2019. Contains 327989 sequences. (Running on oeis4.)