1,3

Also number of 3 X 3 matrices with nonnegative integer entries with zero main diagonal and without zero rows or colums, such that sum of all entries is n. - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 06 2006

A T_1-hypergraph is a hypergraph (not necessarily without empty hyperedges or multiple hyperedges) which for every ordered pair (u,v) of distinct nodes has a hyperedge containing u but not v. A proper hypergraph is a hypergraph without empty hyperedges or hyperedges containing all nodes. - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 06 2006

V. Jovovic and G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, Diskretnaya Matematika, 11 (1999), no. 4, 127-138 (translated in Discrete Mathematics and Applications, 9, (1999), no. 6)

V. Jovovic, G. Kilibarda, On enumeration of the class of all monotone Boolean functions, in preparation.

a(n)=C(n+5, 5)-6*C(n+3, 3)+6*C(n+2, 2)+3*C(n+1, 1)-6*C(n, 0).

a(n+1)= ( n^4 +20*n^3 +35*n^2 -140*n +84 )*n/120.

There are 15 proper T_1-hypergraphs with 3 nodes and 4 hyperedges: {{3},{3},{2},{1}}, {{3},{2},{2},{1}}, {{3},{2},{2,3},{1}}, {{3},{2},{1},{1}}, {{3},{2},{1},{1,3}}, {{3},{2},{1},{1,2}}, {{3},{2},{1,3},{1,2}}, {{3},{2,3},{1},{1,2}}, {{3},{2,3},{1,3},{1,2}}, {{2},{2,3},{1},{1,3}}, {{2},{2,3},{1,3},{1,2}}, {{2,3},{2,3},{1,3},{1,2}}, {{2,3},{1},{1,3},{1,2}}, {{2,3},{1,3},{1,3},{1,2}}, {{2,3},{1,3},{1,2},{1,2}}

Cf. A056005, A047707.

Sequence in context: A007972 A015520 A098520 this_sequence A142861 A088979 A034571

Adjacent sequences: A056075 A056076 A056077 this_sequence A056079 A056080 A056081

nonn

Vladeta Jovovic, Goran Kilibarda (vladeta(AT)eunet.rs), Jul 26 2000