A300648 Number of orderless same-trees of weight n in which all outdegrees are odd.

1, 1, 2, 1, 2, 2, 2, 1, 6, 2, 2, 2, 2, 2, 12, 1, 2, 6, 2, 2, 14, 2, 2, 2, 8, 2, 68, 2, 2, 12, 2, 1, 18, 2, 16, 6, 2, 2, 20, 2, 2, 14, 2, 2, 644, 2, 2, 2, 10, 8, 24, 2, 2, 68, 20, 2, 26, 2, 2, 12, 2, 2, 1386, 1, 22, 18, 2, 2, 30, 16, 2, 6, 2, 2, 4532, 2, 22, 20

Offset

1,3

Comments

An orderless same-tree of weight n > 0 is either a single node of weight n, or a finite multiset of two or more orderless same-trees whose weights are all equal and sum to n.

Links

Antti Karttunen, Table of n, a(n) for n = 1..8192

Formula

a(n) = 1 + Sum_d binomial(a(n/d) + d - 1, d) where the sum is over odd divisors of n greater than 1.

Example

The a(9) = 6 odd orderless same-trees: 9, (333), (33(111)), (3(111)(111)), ((111)(111)(111)), (111111111).

Mathematica

a[n_]:=1+Sum[Binomial[a[n/d]+d-1, d], {d, Select[Rest[Divisors[n]], OddQ]}];
Array[a, 80]

Prog

(PARI) a(n) = if (n==1, 1, 1 + sumdiv(n, d, if ((d > 1) && (d % 2), binomial(a(n/d) + d - 1, d)))); \\ Michel Marcus, Mar 10 2018

Crossrefs

Cf. A003238, A006241, A063834, A069283, A273873, A281145, A289078, A289079, A289501, A298118, A300436, A300439, A300574, A300647, A300649, A300650.

Sequence in context: A290087 A016443 A327640 * A318450 A120256 A300647

Adjacent sequences: A300645 A300646 A300647 * A300649 A300650 A300651

Keyword

nonn,look

Author

Gus Wiseman, Mar 10 2018

Status

approved