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A056182
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First differences of A003063.
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4
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0, 2, 10, 38, 130, 422, 1330, 4118, 12610, 38342, 116050, 350198, 1054690, 3172262, 9533170, 28632278, 85962370, 258018182, 774316690, 2323474358, 6971471650, 20916512102, 62753730610, 188269580438, 564825518530
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Let V be a binary relation on the power set P(A) of a set A having n = |A| elements such that for every element x, y of P(A), xVy if x is a proper subset of y or y is a proper subset of x. Then a(n) = |V|. - Ross La Haye (rlahaye(AT)new.rr.com), Dec 22 2006
It appears that a(n) is the number of permutations p of 1,..,(n+2) such that max[p(i+1)-p(i)] is 2. For example, for n=1, the permutations (1,3,2) and (2,1,3) and no others have the desired property, so a(1)=2. This approach gives values in agreement with all listed terms. [John W. Layman, Nov 09 2011]
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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.
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FORMULA
| 2 * (3^n - 2^n).
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MATHEMATICA
| Table[ -((-1 + k)^(1-k+n)*(-1+k)!)+k^(-k+n)*k! /. k -> 3, {n, 3, 36} ]
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CROSSREFS
| 3rd column of A056151.
A002783(n) - 1.
Sequence in context: A048499 A119358 A110148 * A081956 A120278 A166898
Adjacent sequences: A056179 A056180 A056181 * A056183 A056184 A056185
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Aug 05 2000
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EXTENSIONS
| More terms from Wouter Meeussen (wouter.meeussen(AT)pandora.be), Aug 05 2000
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