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A358904
Number of finite sets of compositions with all equal sums and total sum n.
3
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
0,3
FORMULA
a(n>0) = Sum_{d|n} binomial(2^(d-1),n/d).
EXAMPLE
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)}
MATHEMATICA
Table[If[n==0, 1, Sum[Binomial[2^(d-1), n/d], {d, Divisors[n]}]], {n, 0, 30}]
PROG
(PARI) a(n) = if (n, sumdiv(n, d, binomial(2^(d-1), n/d)), 1); \\ Michel Marcus, Dec 14 2022
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.
Sequence in context: A283015 A264629 A349328 * A283059 A283081 A344265
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 13 2022
STATUS
approved