cp's OEIS Frontend

A383617 Triangle read by rows: T(n,k) is the number of binary relations on a set of n objects, k of which are picked out, 0 <= k <= n.

%I A383617 #14 May 08 2025 03:15:05
%S A383617 1,2,2,10,16,10,104,272,272,104,3044,11456,16960,11456,3044,291968,
%T A383617 1432608,2842304,2842304,1432608,291968,96928992,578431232,1441700480,
%U A383617 1920352256,1441700480,578431232,96928992,112282908928,784780122880,2351993457920,3918054495616,3918054495616,2351993457920,784780122880,112282908928
%N A383617 Triangle read by rows: T(n,k) is the number of binary relations on a set of n objects, k of which are picked out, 0 <= k <= n.
%C A383617 The row sums are the number of simple digraphs with n 4-colored nodes. The colors result from the four cases combining the property self-referencing (yes/no) with "picked out" (yes/no).
%H A383617 Peter Dolland, <a href="/A383617/a383617.py.txt">Python calculation of T(n,k)</a>
%F A383617 T(n,k) = T(n,n-k).
%F A383617 T(n,0) = T(n,n) = A000595(n).
%F A383617 Sum_{k=0..n} T(n,k) = A353996(n+1) = A329874(n,4).
%e A383617 Triangle starts:
%e A383617             1;
%e A383617             2,            2;
%e A383617            10,           16,            10;
%e A383617           104,          272,           272,           104;
%e A383617          3044,        11456,         16960,         11456,          3044;
%e A383617        291968,      1432608,       2842304,       2842304,       1432608,  291968;
%e A383617      96928992,    578431232,    1441700480,    1920352256,    1441700480, ...
%e A383617  112282908928, 784780122880, 2351993457920, 3918054495616, 3918054495616, ...
%e A383617 ...
%e A383617 Example n=2, k=1: The both objects are differentiated. As a consequence all binary relations on two different objects have to be counted: These are the subsets of the cross product of the objects set with itself. This contains four pairs, so the number of subsets is 2^4 = 16.
%Y A383617 Cf. A000595 (edge cases), A353996 (row sums), A329874 (4th column = row sums).
%K A383617 nonn,tabl
%O A383617 0,2
%A A383617 _Peter Dolland_, May 02 2025