A349927
Number of transitive relations on an n-set with exactly three ordered pairs.
Original entry on oeis.org
0, 0, 2, 43, 276, 1150, 3710, 10017, 23688, 50556, 99450, 183095, 319132, 531258, 850486, 1316525, 1979280, 2900472, 4155378, 5834691, 8046500, 10918390, 14599662, 19263673, 25110296, 32368500, 41299050, 52197327, 65396268, 81269426, 100234150
Offset: 0
a(2) = 2. These two transitive relations are {(1,1),(1,2),(2,2)} and {(1,1),(2,1),(2,2)} on the 2-set {1,2}.
A349849
Number of transitive relations on an n-set with exactly four ordered pairs.
Original entry on oeis.org
0, 0, 1, 45, 549, 3755, 18120, 69006, 220710, 616554, 1545435, 3544915, 7552611, 15119325, 28699034, 52032540, 90643260, 152465316, 248625765, 394404489, 610396945, 923906655, 1370595996, 1996425530, 2859913794, 4034751150, 5612802975, 7707539151, 10457928495
Offset: 0
a(2) = binomial(2,2) = 1. The only transitive relation with four ordered pairs on the 2-set {1,2} is {(1,1),(1,2),(2,1),(2,2)}.
A348634
Number of transitive relations on an n-set with exactly five ordered pairs.
Original entry on oeis.org
0, 0, 0, 27, 768, 8771, 63468, 340620, 1470784, 5371002, 17153352, 49075521, 128066400, 309124101, 697874996, 1486830618, 3011414784, 5833686340, 10863883728, 19532496375, 34028554944, 57623258007, 95101946940, 153331834040, 241997811264, 374544148830, 569365964440, 851301035325, 1253479866912, 1819599953913, 2606698902276
Offset: 0
No relation containing exactly five ordered pairs on a 2-element set exists. Thus a(2)=0.
Also, there are 27 transitive relations with exactly five ordered pairs on a 3-set. One such relation is {(1,1),(1,2),(1,3),(2,2),(3,2)} on the 3-set {1,2,3}.
Showing 1-3 of 3 results.