|
| |
|
|
A059052
|
|
Number of n-element unlabeled ordered T_0-antichains; T_1-hypergraphs (with empty hyperedge but without multiple hyperedges) on n labeled nodes.
|
|
10
|
|
|
|
2, 4, 4, 72, 38040, 4020463392, 18438434825136728352, 340282363593610211921722192165556850240, 115792089237316195072053288318104625954343609704705784618785209431974668731584
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,1
|
|
|
COMMENTS
|
An antichain on a set is a T_0-antichain if for every two distinct points of the set there exists a member of the antichain containing one but not the other point. T_1-hypergraph is a hypergraph which for every ordered pair (u,v) of distinct nodes has a hyperedge containing u but not v.
|
|
|
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
|
Table of n, a(n) for n=0..8.
|
|
|
FORMULA
|
a(n)=Sum_{m=0..2^n} A(n, m), where A(n, m) is number of n-element ordered T_0-antichains on an unlabeled m-set. Cf. A059048.
|
|
|
EXAMPLE
|
a(n) = row sums of A059048. a(3) = 2 + 13 + 26 + 22 + 8 + 1. a(6) = 2^64 - 30*2^48 + 120*2^40 + 60*2^36 + 60*2^34 - 12*2^33 - 345*2^32 - 720*2^30 + 810*2^28 + 120*2^27 + 480*2^26 + 360*2^25 - 480*2^24 - 720*2^23 - 240*2^22 - 540*2^21 + 1380*2^20 + 750*2^19 + 60*2^18 - 210*2^17 - 1535*2^16 - 1820*2^15 + 2250*2^14 + 1800*2^13 - 2820*2^12 + 300*2^11 + 2040*2^10 + 340*2^9 - 1815*2^8 + 510*2^7 - 1350*2^6 + 1350*2^5 + 274*2^4 - 548*2^3 + 120*2^2.
|
|
|
CROSSREFS
|
Cf. A059048-A059051.
Sequence in context: A225171 A155952 A145636 * A189882 A065975 A089420
Adjacent sequences: A059049 A059050 A059051 * A059053 A059054 A059055
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Vladeta Jovovic, Goran Kilibarda (vladeta(AT)eunet.rs), Dec 19 2000
|
|
|
STATUS
|
approved
|
| |
|
|
