OFFSET
0,3
COMMENTS
A set-system of weight n is a finite set of finite nonempty sets whose sizes sum to n.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..50
FORMULA
a(p) = 2 for prime p. - Andrew Howroyd, Aug 29 2019
a(n) = Sum_{d|n} A331508(n/d, d) for n > 0. - Andrew Howroyd, Jan 16 2024
EXAMPLE
Non-isomorphic representatives of the a(6) = 10 set-systems:
{{1,2,3,4,5,6}}
{{1,2,3},{4,5,6}}
{{1,2,5},{3,4,5}}
{{1,3,4},{2,3,4}}
{{1,2},{1,3},{2,3}}
{{1,2},{3,4},{5,6}}
{{1,2},{3,5},{4,5}}
{{1,3},{2,4},{3,4}}
{{1,4},{2,4},{3,4}}
{{1},{2},{3},{4},{5},{6}}
PROG
(PARI) \\ See A331508 for T(n, k).
a(n) = {if(n==0, 1, sumdiv(n, d, if(d==1 || d==n, 1, T(n/d, d))))} \\ Andrew Howroyd, Jan 16 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 17 2018
EXTENSIONS
Terms a(12) and beyond from Andrew Howroyd, Sep 01 2019
STATUS
approved