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A056071
Number of 6-element ordered antichains on an unlabeled n-element set; T_1-hypergraphs with 6 labeled nodes and n hyperedges.
3
30, 8340, 780242, 29813578, 657271645, 10037038800, 117733967666, 1130702091428, 9273992351046, 66900184307860, 433616524985590, 2566055594813118, 14037125952339998, 71676448315103924, 344320192201127730, 1566076395413987110, 6779944255517707576
OFFSET
4,1
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).
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).
CROSSREFS
Cf. A051114 for 6-element (unordered) antichains on a labeled n-element set, A056005.
Sequence in context: A087216 A239925 A059049 * A299410 A377221 A294976
KEYWORD
nonn,easy
AUTHOR
Vladeta Jovovic, Goran Kilibarda, Zoran Maksimovic, Jul 26 2000
EXTENSIONS
More terms from Sean A. Irvine, Apr 14 2022
STATUS
approved