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Search: id:A036239
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| A036239 |
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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. |
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27
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| 0, 2, 15, 80, 375, 1652, 7035, 29360, 120975, 494252, 2007555, 8120840, 32753175, 131818052, 529680075, 2125927520, 8525298975, 34165897052, 136857560595, 548011897400, 2193792030375, 8780400395252, 35137296305115, 140596265198480
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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
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REFERENCES
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W. W. Kokko, "Interactions", manuscript, 1983.
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).
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]
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..200
Thomas Wieder, The number of certain k-combinations of an n-set, Applied Mathematics Electronic Notes, vol. 8 (2008).
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FORMULA
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1/2!(4^n-3^n-2^n+1).
a(n) = 3*StirlingS2(n+1,4) + 2*StirlingS2(n+1,3). - Ross La Haye (rlahaye(AT)new.rr.com), Jan 10 2008
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]
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EXAMPLE
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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]
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PROGRAM
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(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]
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CROSSREFS
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Cf. A036240, A051180-A051185.
Cf. A028243, A032263.
A003462, A006516, A016127, A016129, A016130, A016311, A016316, A016321, A016325 [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 05 2009]
Sequence in context: A102289 A041243 A056079 this_sequence A109725 A057152 A002740
Adjacent sequences: A036236 A036237 A036238 this_sequence A036240 A036241 A036242
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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