OFFSET
0,7
COMMENTS
Maximal e for a given n (i.e., the length of the n-th row minus 1) is A002620(n), see Mathematics StackExchange. - Andrey Zabolotskiy, Mar 12 2021
LINKS
R. J. Mathar, Table of T(n,e) for n<=10
Brendan McKay, Digraphs, posets tables at the bottom of the page.
R. J. Mathar, Poset Illustrations
Mathematics StackExchange, Maximum number of comparisons required to define a partial ordering, 2021.
FORMULA
T(n,0) = T(n,1) = 1.
T(n,e) = A022016(e) for n >= 2e.
EXAMPLE
The table starts
1 ;
1 ;
1 1 ;
1 1 3 ;
1 1 4 8 2 ;
1 1 4 11 29 12 5 ;
1 1 4 12 43 105 92 45 12 3 ;
1 1 4 12 46 156 460 582 487 204 71 14 7 ;
1 1 4 12 47 170 670 2097 3822 4514 3271 1579 561 186 44 16 4 ;
...
T(4,0) = 1: the 4-point poset with no relations, 4 isolated points in the Hasse diagram.
T(4,1) = 1: the 4-point poset with one relation, the Hasse diagram has one vertical line and 2 isolated points.
T(4,2) = 4: the 4 posets contributing to A022016(4) = 4, extended by additional isolated point when the number of points is less than 4.
T(4,3) = 8: the 8 posets contributing to A022017(3).
T(4,4) = 2: the "dagaz rune" poset {1<3, 2<3, 1<4, 2<4}
o o
|X|
o o
and the "diamond" poset {1<2, 1<3, 2<4, 3<4}
o
/ \
o o
\ /
o
CROSSREFS
KEYWORD
nonn,tabf,hard
AUTHOR
R. J. Mathar, Mar 12 2021
EXTENSIONS
T(0,0) = 1 prepended and "conjecture" removed from A022016 formula. Andrey Zabolotskiy, Mar 12 2021
STATUS
approved