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A349927
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Number of transitive relations on an n-set with exactly three ordered pairs.
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4
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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
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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) = 2*C(n,2) + 37*C(n,3) + 116*C(n,4) + 180*C(n,5) + 120*C(n,6).
a(n) = (1/6)*(n^6 - 6*n^5 + 24*n^4 - 47*n^3 + 38*n^2 - 10*n).
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EXAMPLE
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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}.
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PROG
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CROSSREFS
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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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