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!)
A289078 Number of orderless same-trees of weight n. 26
1, 2, 2, 5, 2, 9, 2, 22, 6, 11, 2, 94, 2, 13, 12, 334, 2, 205, 2, 210, 14, 17, 2, 7218, 8, 19, 68, 443, 2, 1687, 2, 69109, 18, 23, 16, 167873, 2, 25, 20, 89969, 2, 7041, 2, 1548, 644, 29, 2, 36094795, 10, 3078, 24, 2604, 2, 1484102, 20, 1287306, 26, 35, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

An orderless same-tree t is either: (case 1) a positive integer, or (case 2) a finite multiset of two or more orderless same-trees, all having the same weight. The weight of t in case 1 is the number itself, and in case 2 it is the sum of weights of the branches. For example {{{3,{1,1,1}},{2,{1,1},{1,1}}},{{{1,1,1},{1,1,1}},{{1,1},{1,1},{1,1}}}} is an orderless same-tree of weight 24 with 2 branches.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..2500

FORMULA

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

EXAMPLE

The a(6)=9 orderless same-trees are: 6, (33), (3(111)), (222), (22(11)), (2(11)(11)), ((11)(11)(11)), ((111)(111)), (111111).

MAPLE

with(numtheory):

a:= proc(n) option remember; 1 + add(

      binomial(a(n/d)+d-1, d), d=divisors(n) minus {1})

    end:

seq(a(n), n=1..60);  # Alois P. Heinz, Jul 05 2017

MATHEMATICA

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

Array[a, 100]

PROG

(PARI) seq(n)={my(v=vector(n)); for(n=1, n, v[n] = 1 + sumdiv(n, d, binomial(v[n/d]+d-1, d))); v} \\ Andrew Howroyd, Aug 20 2018

CROSSREFS

Cf. A196545, A273873, A275870, A281145, A281146, A289079.

Sequence in context: A305798 A305808 A266662 * A051612 A083456 A211932

Adjacent sequences:  A289075 A289076 A289077 * A289079 A289080 A289081

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jun 23 2017

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 August 10 22:22 EDT 2020. Contains 336403 sequences. (Running on oeis4.)