A056078 - OEIS

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A056078

Number of proper T_1-hypergraphs with 3 labeled nodes and n hyperedges.

0, 0, 2, 15, 54, 141, 306, 588, 1036, 1710, 2682, 4037, 5874, 8307, 11466, 15498, 20568, 26860, 34578, 43947, 55214, 68649, 84546, 103224, 125028, 150330, 179530, 213057, 251370, 294959, 344346, 400086, 462768, 533016, 611490, 698887 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,3`
	COMMENTS	`Also number of 3 X 3 matrices with nonnegative integer entries with zero main diagonal and without zero rows or columns, 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`
	REFERENCES	`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.`
	FORMULA	`a(n)=C(n+5, 5)-6C(n+3, 3)+6C(n+2, 2)+3C(n+1, 1)-6C(n, 0).` `a(n+1)= ( n^4 +20n^3 +35n^2 -140n +84 )n/120.`
	EXAMPLE	`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}}`
	CROSSREFS	`Cf. A056005, A047707.` `Sequence in context: A007972 A015520 A098520 * A142861 A088979 A034571` `Adjacent sequences: A056075 A056076 A056077 * A056079 A056080 A056081`
	KEYWORD	`nonn`
	AUTHOR	`Vladeta Jovovic, Goran Kilibarda (vladeta(AT)eunet.rs), Jul 26 2000`

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Last modified February 17 02:08 EST 2012. Contains 205978 sequences.