0,2

a(n) = (1/2)(4^n - 3^(n+1) + 5*2^n - 1) = 3*StirlingS2(n+1,4) + StirlingS2(n+1,2) + 1.

a(3) = 11 because for P(A) = {{},{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}} we have for case 0 {{1,2},{1,3}}, {{1,2},{2,3}}, {{1,3},{2,3}} and we have for case 1 {{},{}}, {{1},{1}}, {{2},{2}}, {{3},{3}}, {{1,2},{1,2}}, {{1,3},{1,3}}, {{2,3},{2,3}}, {{1,2,3},{1,2,3}}.

Cf. A032263, A000079.

Sequence in context: A105996 A107703 A114954 this_sequence A120259 A091240 A068488

Adjacent sequences: A134016 A134017 A134018 this_sequence A134020 A134021 A134022

nonn

Ross La Haye (rlahaye(AT)new.rr.com), Jan 10 2008