Search: id:A036239
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%I A036239
%S A036239 0,2,15,80,375,1652,7035,29360,120975,494252,2007555,8120840,32753175,
%T A036239 131818052,529680075,2125927520,8525298975,34165897052,136857560595,
%U A036239 548011897400,2193792030375,8780400395252,35137296305115,140596265198480
%N A036239 Number of 2-element intersecting families of an n-element set; number 
               of 2-way interactions when 2 subsets of power set on {1..n} are chosen 
               at random.
%C A036239 Let P(A) be the power set of an n-element set A. Then a(n) = the number 
               of pairs of elements {x,y} of P(A) for which either 0) x and y are 
               intersecting but 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. - Ross La 
               Haye (rlahaye(AT)new.rr.com), Jan 10 2008
%D A036239 W. W. Kokko, "Interactions", manuscript, 1983.
%D A036239 V. Jovovic, G. Kilibarda, On the number of Boolean functions in the Post 
               classes F^{mu}_8, Diskretnaya Matematika, 11 (1999), no. 4, 127-138 
               (translated in Discrete Mathematics and Applications, 9, (1999), 
               no. 6).
%D A036239 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]
%H A036239 T. D. Noe, <a href="b036239.txt">Table of n, a(n) for n=1..200</a>
%H A036239 Thomas Wieder, The number of certain k-combinations of an n-set, <a href="http:/
               /www.math.nthu.edu.tw/~amen/">Applied Mathematics Electronic Notes</
               a>, vol. 8 (2008).
%F A036239 1/2!(4^n-3^n-2^n+1).
%F A036239 a(n) = 3*StirlingS2(n+1,4) + 2*StirlingS2(n+1,3). - Ross La Haye (rlahaye(AT)new.rr.com), 
               Jan 10 2008
%F A036239 a(n) =(4^n - 2^n)/2-(3^n - 1)/2, n>=1 . a(n) = A006516-A003462 for 1 
               to . [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 05 
               2009]
%e A036239 if n=1 then 1-1=0 ifn =2 then 6-4=2 if n=5 then 496 - 121 = 375 etc... 
               [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 05 2009]
%o A036239 (Other) sage: [(4^n - 2^n)/2-(3^n - 1)/2 for n in xrange(1,24)] # [From 
               Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 05 2009]
%Y A036239 Cf. A036240, A051180-A051185.
%Y A036239 Cf. A028243, A032263.
%Y A036239 A003462, A006516, A016127, A016129, A016130, A016311, A016316, A016321, 
               A016325 [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 
               05 2009]
%Y A036239 Sequence in context: A102289 A041243 A056079 this_sequence A109725 A057152 
               A002740
%Y A036239 Adjacent sequences: A036236 A036237 A036238 this_sequence A036240 A036241 
               A036242
%K A036239 nonn,easy,nice
%O A036239 1,2
%A A036239 N. J. A. Sloane (njas(AT)research.att.com).

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