login
A056070
Number of 5-element ordered antichains on an unlabeled n-element set; T_1-hypergraphs with 5 labeled nodes and n hyperedges.
1
30, 2206, 56242, 766198, 7056249, 49662920, 286860862, 1422695104, 6246302316, 24810260818, 90593318410, 307833736038, 982717917851, 2969842897554, 8548862507642, 23559234462890, 62421788882924, 159585012804848, 394875247007432, 948171537489016
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 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).
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).
CROSSREFS
Cf. A051113 for 5-element (unordered) antichains on a labeled n-element set, A056005.
Sequence in context: A092617 A295446 A056093 * A301377 A054647 A061162
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