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Search: id:A053154
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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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+0
4
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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; listen)
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OFFSET
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0,3
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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 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
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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).
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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) + StirlingS2(n+1,2). - Ross La Haye (rlahaye(AT)new.rr.com), Jan 11 2008
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CROSSREFS
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Cf. A036239.
Equals (A083324(n) - 1)/2.
Cf. A000225, A032263, A028243.
Sequence in context: A026877 A128746 A049675 this_sequence A141222 A127360 A116415
Adjacent sequences: A053151 A053152 A053153 this_sequence A053155 A053156 A053157
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KEYWORD
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easy,nonn
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AUTHOR
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Vladeta Jovovic, Goran Kilibarda (vladeta(AT)Eunet.yu), Feb 28 2000
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