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A306019
Number of non-isomorphic set-systems of weight n in which all parts have the same size.
12
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
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 17 2018
EXTENSIONS
Terms a(12) and beyond from Andrew Howroyd, Sep 01 2019
STATUS
approved