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A028243
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3^(n-1) - 2*2^(n-1) + 1 (essentially Stirling numbers of second kind).
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14
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0, 0, 2, 12, 50, 180, 602, 1932, 6050, 18660, 57002, 173052, 523250, 1577940, 4750202, 14283372, 42915650, 128878020, 386896202, 1161212892, 3484687250, 10456158900, 31372671002, 94126401612
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| For n>=3, a(n) is equal to the number of functions f: {1,2,...,n-1}->{1,2,3} such that Im(f) contains 2 fixed elements. - Aleksandar M. Janjic and Milan R. Janjic (agnus(AT)blic.net), Mar 08 2007
Let P(A) be the power set of an n-element 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 (rlahaye(AT)new.rr.com), Jan 02 2008
Let P(A) be the power set of an n-element 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|. [From Ross La Haye (rlahaye(AT)new.rr.com), Mar 19 2009]
Let P(A) be the power set of an n-element 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|. [From Ross La Haye (rlahaye(AT)new.rr.com), Mar 19 2009]
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REFERENCES
| 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]
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), Mar 19 2009]
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LINKS
| Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
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FORMULA
| a(n)=2*S(n, 3)=2*A000392(n). - Emeric Deutsch (deutsch(AT)duke.poly.edu), 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 (mathar(AT)strw.leidenuniv.nl), Nov 22 2007
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MAPLE
| restart:with (combinat):a:=n->(sum((stirling2(n, 3)), j=2..n)):seq(a(n), n=0..40): b:=n->(sum((stirling2(n, 3)), j=0..n)):seq(b(n), n=0..40):# c:=b-a:seq(c(n), n=1..24); [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 24 2008]
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PROG
| sage: [stirling_number2(i, 3)*2 for i in xrange(1, 30)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 26 2008
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CROSSREFS
| Cf. A000392, A008277.
Sequence in context: A119978 A139234 A039784 * A003493 A197891 A202789
Adjacent sequences: A028240 A028241 A028242 * A028244 A028245 A028246
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Doug McKenzie mckfam4(AT)aol.com
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