A056070 Number of 5-element ordered antichains on an unlabeled n-element set; T_1-hypergraphs with 5 labeled nodes and n hyperedges.

30, 2206, 56242, 766198, 7056249, 49662920, 286860862, 1422695104, 6246302316, 24810260818, 90593318410, 307833736038, 982717917851, 2969842897554, 8548862507642, 23559234462890, 62421788882924, 159585012804848, 394875247007432, 948171537489016

Offset: 4

Author

Vladeta Jovovic, Goran Kilibarda, Zoran Maksimovic, Jul 26 2000

Keywords

• nonn
• easy

Comments

T_1-hypergraph is a hypergraph (not necessarily without empty hyperedges or multiple hyperedges) which for every ordered pair of distinct nodes has a hyperedge containing one but not the other node.

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

Links

• K. S. Brown, Dedekind's problem
• Index entries for linear recurrences with constant coefficients, signature (32, -496, 4960, -35960, 201376, -906192, 3365856, -10518300, 28048800, -64512240, 129024480, -225792840, 347373600, -471435600, 565722720, -601080390, 565722720, -471435600, 347373600, -225792840, 129024480, -64512240, 28048800, -10518300, 3365856, -906192, 201376, -35960, 4960, -496, 32, -1).

Crossrefs

Cf. A051113 for 5-element (unordered) antichains on a labeled n-element set, A056005.

Formula

a(n)=C(n + 31, 31) - 20*C(n + 23, 23) + 60*C(n + 19, 19) + 20*C(n + 17, 17) + 10*C(n + 16, 16) - 110*C(n + 15, 15) - 120*C(n + 14, 14) + 150*C(n + 13, 13) + 120*C(n + 12, 12) - 240*C(n + 11, 11) + 20*C(n + 10, 10) + 240*C(n + 9, 9) + 40*C(n + 8, 8) - 205*C(n + 7, 7) + 60*C(n + 6, 6) - 210*C(n + 5, 5) + 210*C(n + 4, 4) + 50*C(n + 3, 3) - 100*C(n + 2, 2) + 24*C(n + 1, 1).

Extensions

More terms from Sean A. Irvine, Apr 14 2022