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

Author

Gus Wiseman, Apr 26 2018

Keywords

• nonn

Comments

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

Examples

			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}.
		

Crossrefs

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

Programs

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}]