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A134018 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 either x is a subset of y or y is 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. 0
0, 1, 3, 10, 45, 226, 1113, 5230, 23565, 102826, 438273, 1836550, 7601685, 31183426, 127084233, 515429470, 2083077405, 8396552026, 33779262993, 135696871990, 544528258725, 2183337968626, 8749031918553, 35043178292110, 140313885993645, 561679104393226 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..25.

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. [Ross La Haye, Feb 22 2009]

Index entries for linear recurrences with constant coefficients, signature (10,-35,50,-24).

FORMULA

a(n) = (1/2)(4^n - 3^(n+1) + 5*2^n - 3) = 3*StirlingS2(n+1,4) + StirlingS2(n+1,2).

G.f.: x*(1-7*x+15*x^2)/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)). [Colin Barker, Jul 29 2012]

EXAMPLE

a(3) = 10 because for P(A) = {{},{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}} we have for case 0 {{},{1}}, {{},{2}}, {{},{3}}, {{},{1,2}}, {{},{1,3}}, {{},{2,3}}, {{},{1,2,3}} and we have for case 1 {{1,2},{1,3}}, {{1,2},{2,3}}, {{1,3},{2,3}}.

MATHEMATICA

LinearRecurrence[{10, -35, 50, -24}, {0, 1, 3, 10}, 30] (* Harvey P. Dale, Dec 01 2017 *)

CROSSREFS

Cf. A000225, A032263.

Sequence in context: A096752 A293554 A211193 * A028417 A060311 A184947

Adjacent sequences:  A134015 A134016 A134017 * A134019 A134020 A134021

KEYWORD

nonn,easy

AUTHOR

Ross La Haye, Jan 10 2008

EXTENSIONS

More terms from Harvey P. Dale, Dec 01 2017

STATUS

approved

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Last modified June 15 12:29 EDT 2021. Contains 345048 sequences. (Running on oeis4.)