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 A134063 a(n) = (1/2)*(3^n - 2^(n+1) + 3). 0
 1, 1, 2, 7, 26, 91, 302, 967, 3026, 9331, 28502, 86527, 261626, 788971, 2375102, 7141687, 21457826, 64439011, 193448102, 580606447, 1742343626, 5228079451, 15686335502, 47063200807, 141197991026, 423610750291, 1270865805302, 3812664524767, 11438127792026 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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, Jul 06 2009] LINKS 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. [Ross La Haye, Feb 22 2009] Index entries for linear recurrences with constant coefficients, signature (6,-11,6) FORMULA a(n) = 3*StirlingS2(n,3) + StirlingS2(n,2) + 1. a(n) = StirlingS2(n+1,3) + 1. - Ross La Haye, Jan 21 2008 a(n) = 6 a(n-1)-11 a(n-2) +6 a(n-3) (n >= 3). Also a(n) = 4 a(n-1)-3 a(n-2)+ 2^{n-2} (n >= 3). - 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). [R. J. Mathar, Jul 06 2009] EXAMPLE 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}}. MAPLE f := n -> (1/2)*(3^n - 2^(n+1) + 3); MATHEMATICA Table[(3^n-2^(n+1)+3)/2, {n, 0, 30}] (* or *) LinearRecurrence[{6, -11, 6}, {1, 1, 2}, 30] (* Harvey P. Dale, May 05 2020 *) CROSSREFS Cf. A000392, A028243, A000079. Sequence in context: A212961 A000697 A027417 * A087448 A289449 A188860 Adjacent sequences:  A134060 A134061 A134062 * A134064 A134065 A134066 KEYWORD nonn AUTHOR Ross La Haye, Jan 11 2008 EXTENSIONS Edited by N. J. A. Sloane, Jul 06 2009 STATUS approved

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Last modified July 6 16:17 EDT 2020. Contains 335478 sequences. (Running on oeis4.)