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A349919
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Number of transitive relations on an n-set with exactly two ordered pairs.
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3
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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
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OFFSET
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0,3
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LINKS
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FORMULA
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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).
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EXAMPLE
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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)}.
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MATHEMATICA
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LinearRecurrence[{5, -10, 10, -5, 1}, {0, 0, 5, 27, 90}, 50] (* Harvey P. Dale, Oct 23 2022 *)
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CROSSREFS
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This is a diagonal of the array A285192.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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