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A349919
Number of transitive relations on an n-set with exactly two ordered pairs.
3
0, 0, 5, 27, 90, 230, 495, 945, 1652, 2700, 4185, 6215, 8910, 12402, 16835, 22365, 29160, 37400, 47277, 58995, 72770, 88830, 107415, 128777, 153180, 180900, 212225, 247455, 286902, 330890, 379755, 433845, 493520, 559152, 631125, 709835, 795690, 889110, 990527, 1100385, 1219140, 1347260, 1485225, 1633527, 1792670
OFFSET
0,3
LINKS
Firdous Ahmad Mala, Counting Transitive Relations with Two Ordered Pairs, Journal of Applied Mathematics and Computation, 5(4), 247-251.
FORMULA
a(n) = 5*C(n,2) + 12*C(n,3) + 12*C(n,4).
a(n) = (1/2)*(n^4 - 2*n^3 + 4*n^2 - 3).
a(n) = A336535(n) - 1.
EXAMPLE
a(2) = 5. The five relations on a 2-set are {(1,1),(1,2)}, {(1,1),(2,1)}, {(1,1),(2,2)}, {(1,2),(2,2)} and {(2,1),(2,2)}.
MATHEMATICA
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 0, 5, 27, 90}, 50] (* Harvey P. Dale, Oct 23 2022 *)
CROSSREFS
This is a diagonal of the array A285192.
Sequence in context: A135713 A085740 A338996 * A212783 A226315 A201436
KEYWORD
nonn,easy
AUTHOR
Firdous Ahmad Mala, Dec 05 2021
STATUS
approved