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A134169
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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 x is not a subset of y and y is not 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, or 3) x = y.
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1
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1, 2, 7, 29, 121, 497, 2017, 8129, 32641, 130817, 523777, 2096129, 8386561, 33550337, 134209537, 536854529, 2147450881, 8589869057, 34359607297, 137438691329, 549755289601, 2199022206977, 8796090925057, 35184367894529
(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
| Index entries related to linear recurrences with constant coefficients, signature (7,-14,8). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 15 2010]
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FORMULA
| a(n) = 2^(n-1)*(2^n - 1) + 1 = StirlingS2(2^n,2^n - 1) + 1 = C(2^n,2) + 1 = A006516(n) + 1.
a(n)= 7*a(n-1) -14*a(n-2) +8*a(n-3). G.f.: (1-5*x+7*x^2)/((1-x) * (2*x-1) * (4*x-1)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 15 2010]
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EXAMPLE
| a(2) = 7 because for P(A) = {{},{1},{2},{1,2}} we have for case 0
{{1},{2}} and we have for case 2 {{1},{1,2}}, {{2},{1,2}} and we have for
case 3 {{},{}}, {{1},{1}}, {{2},{2}}, {{1,2},{1,2}}. There are 0 {x,y} of
P(A) in this example that fall under case 1.
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MATHEMATICA
| Table[EulerE[2, 2^n], {n, 0, 60}]/2+1 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 03 2009]
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CROSSREFS
| Cf. A000392, A032263, A028243, A000079, A006516.
Sequence in context: A203969 A199581 A120757 * A052961 A150662 A126568
Adjacent sequences: A134166 A134167 A134168 * A134170 A134171 A134172
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KEYWORD
| nonn
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AUTHOR
| Ross La Haye (rlahaye(AT)new.rr.com), Jan 12 2008 Ross
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EXTENSIONS
| More terms and Mathematica program Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 03 2009
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