0,3

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

The inverse binomial transform yields A033484 with another leading 1. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 06 2009]

Ross La Haye, Binary Relations on the Power Set of an n-Element Set, Journal of Integer Sequences, Vol. 12 (2009), Article 09.2.6. [From Ross La Haye (rlahaye(AT)new.rr.com), Feb 22 2009]

a(n) = 3*StirlingS2(n,3) + StirlingS2(n,2) + 1.

a(n) = StirlingS2(n+1,3) + 1. - Ross La Haye (rlahaye(AT)new.rr.com), Jan 21 2008

a(n) = 6 a(n-1)-11 a(n-2) +6 a(n-3) (n > = 3) with a(0) = a(1) = 1, a(2) = 2. Also a(n) = 4 a(n-1)-3 a(n-2)+ 2^{n-2} (n > = 3) with a(0) = a(1) = 1. - Tian-Xiao He (the(AT)iwu.edu), Jul 02 2009

G.f.: -(1-4*x+6*x^2)/((x-1)*(3*x-1)*(2*x-1)). a(n+1)-a(n)=A001047(n+1). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 06 2009]

a(3) = 7 because for P(A) = {{},{1},{2},{1,2}} we have: case 0 {{1},{2}}, case 1 {{1},{1,2}}, {2},{1,2}}, case 2 {{},{}}, {{1},{1}}, {{2},{2}}, {{1,2},{1,2}}.

f := n -> (1/2)*(3^n - 2^(n+1) + 3);

Cf. A000392, A028243, A000079.

Sequence in context: A091145 A000697 A027417 this_sequence A087448 A129273 A055988

Adjacent sequences: A134060 A134061 A134062 this_sequence A134064 A134065 A134066

nonn

Ross La Haye (rlahaye(AT)new.rr.com), Jan 11 2008

Edited by N. J. A. Sloane, Jul 06 2009