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 A028243 a(n) = 3^(n-1) - 2*2^(n-1) + 1 (essentially Stirling numbers of second kind). 25
 0, 0, 2, 12, 50, 180, 602, 1932, 6050, 18660, 57002, 173052, 523250, 1577940, 4750202, 14283372, 42915650, 128878020, 386896202, 1161212892, 3484687250, 10456158900, 31372671002, 94126401612 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS For n >= 3, a(n) is equal to the number of functions f: {1,2,...,n-1} -> {1,2,3} such that Im(f) contains 2 fixed elements. - Aleksandar M. Janjic and Milan Janjic, Mar 08 2007 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 x and y are intersecting and for which either x is a proper subset of y or y is a proper subset of x. - Ross La Haye, Jan 02 2008 Let P(A) be the power set of an n-element set A and R be a relation on P(A) such that for all x, y of P(A), xRy if x is not a subset of y and y is not a subset of x and x and y are disjoint. Then a(n+1) = |R|. - Ross La Haye, Mar 19 2009 Let P(A) be the power set of an n-element set A and R be a relation on P(A) such that for all x, y of P(A), xRy if either 0) x is a proper subset of y or y is a proper subset of x, or 1) x is not a subset of y and y is not a subset of x and x and y are disjoint. Then a(n+2) = |R|. - Ross La Haye, Mar 19 2009 LINKS Seiichi Manyama, Table of n, a(n) for n = 1..2096 O. Bagdasar, On some functions involving the lcm and gcd of integer tuples, Scientific Publications of the State University of Novi Pazar, Appl. Maths. Inform. and Mech., Vol. 6, 2 (2014), 91-100. J. Brandts and C. Cihangir, Counting triangles that share their vertices with the unit n-cube, in Conference Applications of Mathematics 2013 in honor of the 70th birthday of Karel Segeth. Jan Brandts, Sergey Korotov, et al., eds., Institute of Mathematics AS CR, Prague 2013. K. S. Immink, Coding Schemes for Multi-Level Channels that are Intrinsically Resistant Against Unknown Gain and/or Offset Using Reference Symbols, Electronics Letters, Volume: 50, Issue: 1, January 2 2014. Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets [Broken link] 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. FORMULA a(n) = 2*S(n, 3) = 2*A000392(n). - Emeric Deutsch, May 02 2004 G.f.: -2*x^3/(-1+x)/(-1+3*x)/(-1+2*x) = -1/3 - (1/3)/(-1+3*x) + 1/(-1+2*x) - 1/(-1+x). - R. J. Mathar, Nov 22 2007 E.g.f.: (exp(3*x) - 3*exp(2*x) + 3*exp(x) - 1)/3, with a(0) = 0. - Wolfdieter Lang, May 03 2017 MATHEMATICA Table[2 StirlingS2[n, 3], {n, 24}] (* or *) Table[3^(n - 1) - 2*2^(n - 1) + 1, {n, 24}] (* or *) Rest@ CoefficientList[Series[-2 x^3/(-1 + x)/(-1 + 3 x)/(-1 + 2 x), {x, 0, 24}], x] (* Michael De Vlieger, Sep 24 2016 *) PROG (Sage) [stirling_number2(i, 3)*2 for i in xrange(1, 30)] # Zerinvary Lajos, Jun 26 2008 (MAGMA) [3^(n-1) - 2*2^(n-1) + 1: n in [1..30]]; // G. C. Greubel, Nov 19 2017 (PARI) for(n=1, 30, print1(3^(n-1) - 2*2^(n-1) + 1, ", ")) \\ G. C. Greubel, Nov 19 2017 CROSSREFS Cf. A000392, A008277, A163626. Sequence in context: A119978 A139234 A039784 * A003493 A197891 A259802 Adjacent sequences:  A028240 A028241 A028242 * A028244 A028245 A028246 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Doug McKenzie (mckfam4(AT)aol.com) STATUS approved

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