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A300913 Number of non-isomorphic connected set-systems of weight n. 55
1, 1, 1, 2, 4, 7, 18, 37, 96, 239, 658, 1810, 5358, 16057, 50373, 161811, 536964, 1826151, 6380481, 22822280, 83587920, 312954111, 1197178941, 4674642341, 18620255306, 75606404857, 312763294254, 1317356836235, 5646694922172, 24618969819915, 109125629486233, 491554330852608 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
The weight of a set-system is the sum of cardinalities of the sets. Weight is generally not the same as number of vertices.
LINKS
Jean-François Alcover, Table of n, a(n) for n = 0..50 [using Andrew Howroyd's b-file for A283877]
FORMULA
Inverse Euler transform of A283877.
EXAMPLE
Non-isomorphic representatives of the a(1) = 1 through a(5) = 7 set systems:
1: {{1}}
2: {{1,2}}
3: {{1,2,3}}
{{2},{1,2}}
4: {{1,2,3,4}}
{{3},{1,2,3}}
{{1,3},{2,3}}
{{1},{2},{1,2}}
5: {{1,2,3,4,5}}
{{4},{1,2,3,4}}
{{1,4},{2,3,4}}
{{2,3},{1,2,3}}
{{2},{3},{1,2,3}}
{{2},{1,3},{2,3}}
{{3},{1,3},{2,3}}
Non-isomorphic representatives of the a(6) = 18 connected set-systems:
{{1,2,3,4,5,6}}
{{5},{1,2,3,4,5}}
{{1,5},{2,3,4,5}}
{{3,4},{1,2,3,4}}
{{1,2,5},{3,4,5}}
{{1,3,4},{2,3,4}}
{{1},{1,4},{2,3,4}}
{{1},{2,3},{1,2,3}}
{{3},{4},{1,2,3,4}}
{{3},{1,4},{2,3,4}}
{{3},{2,3},{1,2,3}}
{{4},{1,4},{2,3,4}}
{{1,2},{1,3},{2,3}}
{{1,3},{2,4},{3,4}}
{{1,4},{2,4},{3,4}}
{{1},{2},{3},{1,2,3}}
{{1},{2},{1,3},{2,3}}
{{2},{3},{1,3},{2,3}}
MATHEMATICA
A283877 = Import["https://oeis.org/A283877/b283877.txt", "Table"][[All, 2]];
(* EulerInvTransform is defined in A022562 *)
{1} ~Join~ EulerInvTransform[A283877 // Rest] (* Jean-François Alcover, Nov 07 2019, updated Mar 17 2020 *)
CROSSREFS
Sequence in context: A103032 A215649 A259351 * A232484 A223013 A276027
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 19 2018
EXTENSIONS
a(11)-a(31) from Jean-François Alcover, Nov 07 2019
STATUS
approved

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Last modified April 25 11:03 EDT 2024. Contains 371967 sequences. (Running on oeis4.)