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A133224
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Let P(A) denote the power set of an n-element set A. Then a(n) = the sum of the sizes of the union of x and y for every x, y in P(A).
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1
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0, 2, 14, 78, 400, 1960, 9312, 43232, 197120, 885888, 3934720, 17307136, 75509760, 327182336, 1409343488, 6039920640, 25770065920, 109522223104, 463857647616, 1958507577344, 8246342451200
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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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]
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..300
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FORMULA
| a(n) = n*(2^(n-2) + 3*2^(2*n-3)).
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EXAMPLE
| a(2) = 14 because for P(A) = {{},{1},{2},{1,2}} |{} union {1}| = 1, |{} union {2}| = 1, |{} union {1,2}| = 2, |{1} union {2}| = 2, |{1} union {1,2}| = 2 and |{2} union {1,2}| = 2, |{} union {}| = 0, |{1} union {1}| = 1, |{2} union {2}| = 1, |{1,2} union {1,2}| = 2, which sums to 14.
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PROG
| (MAGMA) [n*(2^(n-2) + 3*2^(2*n-3)): n in [0..30]]; // Vincenzo Librandi, Jun 10 2011
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CROSSREFS
| Cf. A027471, A002697, A082134.
Sequence in context: A104871 A172060 A034573 * A183577 A121200 A112408
Adjacent sequences: A133221 A133222 A133223 * A133225 A133226 A133227
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KEYWORD
| nonn
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AUTHOR
| Ross La Haye (rlahaye(AT)new.rr.com), Dec 30 2007, Jan 03 2008
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