login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A300648 Number of orderless same-trees of weight n in which all outdegrees are odd. 4
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 (list; graph; refs; listen; history; text; internal format)
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,changed

AUTHOR

Gus Wiseman, Mar 10 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 13 17:44 EDT 2021. Contains 345008 sequences. (Running on oeis4.)