A306019 Number of non-isomorphic set-systems of weight n in which all parts have the same size.

1, 1, 2, 2, 4, 2, 10, 2, 17, 14, 33, 2, 167, 2, 186, 491, 785, 2, 5839, 2, 11123, 53454, 15229, 2, 1102924, 53537, 193382, 16334183, 12411062, 2, 382413555, 2, 993814248, 9763321547, 53394774, 1778595972, 402119882757, 2, 1111261718, 9674133468473, 16955983996383

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

Cf. A000005, A001315, A007716, A038041, A049311, A283877, A298422, A306017, A306018, A306020, A306021.

Sequence in context: A053204 A152061 A103314 * A194560 A111741 A111793

Adjacent sequences: A306016 A306017 A306018 * A306020 A306021 A306022

Keyword

nonn

Author

Gus Wiseman, Jun 17 2018

Extensions

Terms a(12) and beyond from Andrew Howroyd, Sep 01 2019

Status

approved