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Search: id:A038721
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| 2, 18, 110, 570, 2702, 12138, 52670, 223290, 931502, 3842058, 15718430, 63928410, 258885902, 1045076778, 4208939390, 16921719930, 67944897902, 272553908298, 1092539107550, 4377127901850, 17529428119502, 70180466208618
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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For n>=1, a(n) is equal to the number of functions f: {1,2,...,n+1}->{1,2,3,4} such that Im(f) contains 2 fixed elements. - Aleksandar M. Janjic and Milan R. Janjic (agnus(AT)blic.net), Feb 27 2007
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. Then a(n+1) = |R|. [From Ross La Haye (rlahaye(AT)new.rr.com), Mar 19 2009]
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REFERENCES
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R. B. Nelsen and H. Schmidt, Jr., Chains in power sets, Math. Mag., 64 (1991), 23-31.
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
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Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
Index entries for sequences related to posets
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FORMULA
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4^(n+1) - 2*3^(n+1) + 2^(n+1).
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CROSSREFS
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Cf. A038720.
Sequence in context: A101570 A006043 A112328 this_sequence A064837 A027433 A153338
Adjacent sequences: A038718 A038719 A038720 this_sequence A038722 A038723 A038724
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), May 02 2000
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), May 09 2000
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