

A134165


Let P(A) be the power set of an nelement 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 either x is a subset of y or y is a subset of x, or 1) x and y are disjoint and for which x is not a subset of y and y is not a subset of x, or 2) x and y are intersecting but for which x is not a subset of y and y is not a subset of x, or 3) x = y.


0



1, 3, 8, 24, 86, 348, 1478, 6324, 26846, 112668, 467798, 1925124, 7867406, 31980588, 129475718, 522603924, 2104600766, 8461122108, 33972973238, 136278002724, 546271650926
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OFFSET

0,2


LINKS

Table of n, a(n) for n=0..20.
Ross La Haye, Binary Relations on the Power Set of an nElement Set, Journal of Integer Sequences, Vol. 12 (2009), Article 09.2.6.
Index entries for linear recurrences with constant coefficients, signature (10,35,50,24).


FORMULA

a(n) = (1/2)(4^n  2*3^n + 5*2^n  2) = 3*StirlingS2(n+1,4) + StirlingS2(n+1,3) + 2*StirlingS2(n+1,2) + 1.
G.f.: (17*x+13*x^2x^3)/((1x)*(12*x)*(13*x)*(14*x)). [Colin Barker, Jul 30 2012]


EXAMPLE

a(2) = 8 because for P(A) = {{},{1},{2},{1,2}} we have for case 0 {{},{1}}, {{},{2}}, {{},{1,2}} and we have for case 1 {{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 2.


MATHEMATICA

LinearRecurrence[{10, 35, 50, 24}, {1, 3, 8, 24}, 30] (* Harvey P. Dale, Feb 29 2020 *)


CROSSREFS

Cf. A000225, A000392, A032263, A000079.
Sequence in context: A242985 A148787 A125655 * A071016 A174662 A002104
Adjacent sequences: A134162 A134163 A134164 * A134166 A134167 A134168


KEYWORD

nonn,easy


AUTHOR

Ross La Haye, Jan 12 2008


STATUS

approved



