A303552 Number of periodic multisets of compositions of total weight n.

0, 1, 1, 3, 1, 9, 1, 18, 7, 44, 1, 119, 1, 246, 48, 585, 1, 1470, 1, 3248, 250, 7535, 1, 18114, 42, 40593, 1373, 93726, 1, 218665, 1, 493735, 7539, 1127981, 285, 2587962, 1, 5841445, 40597, 13244166, 1, 30047413, 1, 67604050, 216745, 152258273, 1, 342747130

Offset

1,4

Comments

A multiset is periodic if its multiplicities have a common divisor greater than 1.

Links

Table of n, a(n) for n=1..48.

Example

The a(6) = 9 periodic multisets of compositions are:
{1,1,1,1,1,1},
{1,1,2,2}, {1,1,11,11},
{2,2,2}, {11,11,11},
{3,3}, {21,21}, {12,12}, {111,111}.

Mathematica

nn=60;
ser=Product[1/(1-x^n)^2^(n-1), {n, nn}]
Table[SeriesCoefficient[ser, {x, 0, n}]-Sum[MoebiusMu[d]*SeriesCoefficient[ser, {x, 0, n/d}], {d, Divisors[n]}], {n, 1, nn}]

Crossrefs

Cf. A000740, A000837, A007716, A007916, A034691, A100953, A255906, A269134, A301700, A303386, A303431, A303547, A303551.

Sequence in context: A200006 A070894 A090261 * A130599 A157674 A360752

Adjacent sequences: A303549 A303550 A303551 * A303553 A303554 A303555

Keyword

nonn

Author

Gus Wiseman, Apr 26 2018

Status

approved