A358904 Number of finite sets of compositions with all equal sums and total sum n.

1, 1, 2, 4, 9, 16, 38, 64, 156, 260, 632, 1024, 2601, 4096, 10208, 16944, 40966, 65536, 168672, 262144, 656980, 1090240, 2620928, 4194304, 10862100, 16781584, 41940992, 69872384, 168403448, 268435456, 693528552, 1073741824, 2695006177, 4473400320, 10737385472

Offset: 0

Author

Gus Wiseman, Dec 13 2022

Keywords

• nonn

Examples

			The a(1) = 1 through a(4) = 9 sets:
  {(1)}  {(2)}   {(3)}    {(4)}
         {(11)}  {(12)}   {(13)}
                 {(21)}   {(22)}
                 {(111)}  {(31)}
                          {(112)}
                          {(121)}
                          {(211)}
                          {(1111)}
                          {(2),(11)}
		

Crossrefs

This is the constant-sum case of A098407, ordered A358907.

The version for distinct sums is A304961, ordered A336127.

Allowing repetition gives A305552, ordered A074854.

The case of sets of partitions is A359041.

A001970 counts multisets of partitions.

A034691 counts multisets of compositions, ordered A133494.

A261049 counts sets of partitions, ordered A358906.

Cf. A000009, A063834, A075900, A218482, A296122.

Programs

Mathematica

Table[If[n==0,1,Sum[Binomial[2^(d-1),n/d],{d,Divisors[n]}]],{n,0,30}]

PARI

a(n) = if (n, sumdiv(n, d, binomial(2^(d-1), n/d)), 1); \\ Michel Marcus, Dec 14 2022

Formula

a(n>0) = Sum_{d|n} binomial(2^(d-1),n/d).