Let P(A) be the power set of an n-element set A. Then a(n) = the number of pairs of elements {x,y} of P(A) for which either 0) x and y are disjoint and for which either x is a subset of y or y is a subset of x, or 1) x and y are intersecting but for which x is not a subset of y and y is not a subset of x.
a(3) = 10 because for P(A) = {{},{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}} we have for case 0 {{},{1}}, {{},{2}}, {{},{3}}, {{},{1,2}}, {{},{1,3}}, {{},{2,3}}, {{},{1,2,3}} and we have for case 1 {{1,2},{1,3}}, {{1,2},{2,3}}, {{1,3},{2,3}}.
