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A053154
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Number of 2-element intersecting families (with not necessary distinct sets) of an n-element set.
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6
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0, 1, 5, 22, 95, 406, 1715, 7162, 29615, 121486, 495275, 2009602, 8124935, 32761366, 131834435, 529712842, 2125993055, 8525430046, 34166159195, 136858084882, 548012945975, 2193794127526, 8780404589555, 35137304693722
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| 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 disjoint and for which either x is a subset of y or y is a subset of x, or 1) x and y are intersecting but for which x is not a subset of y and y is not a subset of x, or 2) 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 11 2008
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REFERENCES
| 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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FORMULA
| 1/2!*(4^n-3^n+2^n-1)
a(n) = 3*StirlingS2(n+1,4) + 2*StirlingS2(n+1,3) + StirlingS2(n+1,2). - Ross La Haye (rlahaye(AT)new.rr.com), Jan 11 2008
From Wolfdieter Lang, Oct 28 2011 (Start)
E.g.f.: sum((-1)^j*exp(j*x),j=1..4)/2 = exp(x)*(exp(4*x)-1)/(exp(x)+1)/2.
O.g.f.: sum(((-1)^j)/(1-j*x),j=1..4)/2 = x*(1-5*x+7*x^2)/product(1-j*x,j=1..4). See A196847.
(End)
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CROSSREFS
| Cf. A036239.
Equals (A083324(n) - 1)/2.
Cf. A000225, A032263, A028243.
Sequence in context: A026877 A128746 A049675 * A141222 A127360 A116415
Adjacent sequences: A053151 A053152 A053153 * A053155 A053156 A053157
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KEYWORD
| easy,nonn
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AUTHOR
| Vladeta Jovovic, Goran Kilibarda (vladeta(AT)eunet.rs), Feb 28 2000
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