A056071 Number of 6-element ordered antichains on an unlabeled n-element set; T_1-hypergraphs with 6 labeled nodes and n hyperedges.

30, 8340, 780242, 29813578, 657271645, 10037038800, 117733967666, 1130702091428, 9273992351046, 66900184307860, 433616524985590, 2566055594813118, 14037125952339998, 71676448315103924, 344320192201127730, 1566076395413987110, 6779944255517707576

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

Links

• K. S. Brown, Dedekind's problem
• Eric Weisstein's World of Mathematics, Antichain covers
• Index entries for linear recurrences with constant coefficients, signature (64, -2016, 41664, -635376, 7624512, -74974368, 621216192, -4426165368, 27540584512, -151473214816, 743595781824, -3284214703056, 13136858812224, -47855699958816, 159518999862720, -488526937079580, 1379370175283520, -3601688791018080, 8719878125622720, -19619725782651120, 41107996877935680, -80347448443237920, 146721427591999680, -250649105469666120, 401038568751465792, -601557853127198688, 846636978475316672, -1118770292985239888, 1388818294740297792, -1620288010530347424, 1777090076065542336, -1832624140942590534, 1777090076065542336, -1620288010530347424, 1388818294740297792, -1118770292985239888, 846636978475316672, -601557853127198688, 401038568751465792, -250649105469666120, 146721427591999680, -80347448443237920, 41107996877935680, -19619725782651120, 8719878125622720, -3601688791018080, 1379370175283520, -488526937079580, 159518999862720, -47855699958816, 13136858812224, -3284214703056, 743595781824, -151473214816, 27540584512, -4426165368, 621216192, -74974368, 7624512, -635376, 41664, -2016, 64, -1).

Crossrefs

Cf. A051114 for 6-element (unordered) antichains on a labeled n-element set, A056005.

Formula

a(n)=C(n + 63, 63) - 30*C(n + 47, 47) + 120*C(n + 39, 39) + 60*C(n + 35, 35) + 60*C(n + 33, 33) - 12*C(n + 32, 32) - 345*C(n + 31, 31) - 720*C(n + 29, 29) + 810*C(n + 27, 27) + 120*C(n + 26, 26) + 480*C(n + 25, 25) + 360*C(n + 24, 24) - 480*C(n + 23, 23) - 720*C(n + 22, 22) - 240*C(n + 21, 21) - 540*C(n + 20, 20) + 1380*C(n + 19, 19) + 750*C(n + 18, 18) + 60*C(n + 17, 17) - 210*C(n + 16, 16) - 1535*C(n + 15, 15) - 1820*C(n + 14, 14) + 2250*C(n + 13, 13) + 1800*C(n + 12, 12) - 2820*C(n + 11, 11) + 300*C(n + 10, 10) + 2040*C(n + 9, 9) + 340*C(n + 8, 8) - 1815*C(n + 7, 7) + 510*C(n + 6, 6) - 1350*C(n + 5, 5) + 1350*C(n + 4, 4) + 274*C(n + 3, 3) - 548*C(n + 2, 2) + 120*C(n + 1, 1).

Extensions

More terms from Sean A. Irvine, Apr 14 2022