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%I #55 Jul 11 2024 05:32:15
%S 0,0,5,27,90,230,495,945,1652,2700,4185,6215,8910,12402,16835,22365,
%T 29160,37400,47277,58995,72770,88830,107415,128777,153180,180900,
%U 212225,247455,286902,330890,379755,433845,493520,559152,631125,709835,795690,889110,990527,1100385,1219140,1347260,1485225,1633527,1792670
%N Number of transitive relations on an n-set with exactly two ordered pairs.
%H Firdous Ahmad Mala, <a href="http://dx.doi.org/10.26855/jamc.2021.12.002">Counting Transitive Relations with Two Ordered Pairs</a>, Journal of Applied Mathematics and Computation, 5(4), 247-251.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F a(n) = 5*C(n,2) + 12*C(n,3) + 12*C(n,4).
%F a(n) = (1/2)*(n^4 - 2*n^3 + 4*n^2 - 3).
%F a(n) = A336535(n) - 1.
%e 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)}.
%t LinearRecurrence[{5,-10,10,-5,1},{0,0,5,27,90},50] (* _Harvey P. Dale_, Oct 23 2022 *)
%Y Cf. A006905, A349927, A336535.
%Y This is a diagonal of the array A285192.
%K nonn,easy
%O 0,3
%A _Firdous Ahmad Mala_, Dec 05 2021