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A134169 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. +0
1
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; listen)
OFFSET

0,2

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]

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.

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.

MATHEMATICA

Table[EulerE[2, 2^n], {n, 0, 60}]/2+1 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 03 2009]

CROSSREFS

Cf. A000392, A032263, A028243, A000079, A006516.

Sequence in context: A166939 A155186 A120757 this_sequence A052961 A150662 A126568

Adjacent sequences: A134166 A134167 A134168 this_sequence A134170 A134171 A134172

KEYWORD

nonn

AUTHOR

Ross La Haye (rlahaye(AT)new.rr.com), Jan 12 2008 Ross

EXTENSIONS

More terms and Mathematica program Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 03 2009

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Last modified December 7 23:50 EST 2009. Contains 170430 sequences.


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