A349927 Number of transitive relations on an n-set with exactly three ordered pairs.
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
Examples
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}.
Links
- Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
Programs
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PARI
A349927(n) = (1/6)*(n^6 - 6*n^5 + 24*n^4 - 47*n^3 + 38*n^2 - 10*n); \\ Antti Karttunen, Dec 05 2021
Formula
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).