

A028243


a(n) = 3^(n1)  2*2^(n1) + 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
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OFFSET

1,3


COMMENTS

For n >= 3, a(n) is equal to the number of functions f: {1,2,...,n1} > {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 nelement 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 nelement 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 nelement 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), 91100.
J. Brandts and C. Cihangir, Counting triangles that share their vertices with the unit ncube, 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 MultiLevel 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 nElement 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^(n1)  2*2^(n1) + 1: n in [1..30]]; // G. C. Greubel, Nov 19 2017
(PARI) for(n=1, 30, print1(3^(n1)  2*2^(n1) + 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



