login
This site is supported by donations to The OEIS Foundation.

 

Logo

The October issue of the Notices of the Amer. Math. Soc. has an article about the OEIS.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A134063 a(n) = (1/2)*(3^n - 2^(n+1) + 3). 0
1, 1, 2, 7, 26, 91, 302, 967, 3026, 9331, 28502, 86527, 261626, 788971, 2375102, 7141687, 21457826, 64439011, 193448102, 580606447, 1742343626, 5228079451, 15686335502, 47063200807, 141197991026, 423610750291, 1270865805302, 3812664524767, 11438127792026 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Let P(A) be the power set of an n-element set A. Then a(n-1) = 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 and for which either x is a proper subset of y or y is a proper subset of x, or 2) x = y.

The inverse binomial transform yields A033484 with another leading 1. [From R. J. Mathar, Jul 06 2009]

LINKS

Table of n, a(n) for n=0..28.

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 (6,-11,6)

FORMULA

a(n) = 3*StirlingS2(n,3) + StirlingS2(n,2) + 1.

a(n) = StirlingS2(n+1,3) + 1. - Ross La Haye, Jan 21 2008

a(n) = 6 a(n-1)-11 a(n-2) +6 a(n-3) (n >= 3). Also a(n) = 4 a(n-1)-3 a(n-2)+ 2^{n-2} (n >= 3). - Tian-Xiao He (the(AT)iwu.edu), Jul 02 2009

G.f.: -(1-4*x+6*x^2)/((x-1)*(3*x-1)*(2*x-1)). a(n+1)-a(n)=A001047(n+1). [R. J. Mathar, Jul 06 2009]

EXAMPLE

a(3) = 7 because for P(A) = {{},{1},{2},{1,2}} we have: case 0 {{1},{2}}, case 1 {{1},{1,2}}, {2},{1,2}}, case 2 {{},{}}, {{1},{1}}, {{2},{2}}, {{1,2},{1,2}}.

MAPLE

f := n -> (1/2)*(3^n - 2^(n+1) + 3);

CROSSREFS

Cf. A000392, A028243, A000079.

Sequence in context: A212961 A000697 A027417 * A087448 A289449 A188860

Adjacent sequences:  A134060 A134061 A134062 * A134064 A134065 A134066

KEYWORD

nonn

AUTHOR

Ross La Haye, Jan 11 2008

EXTENSIONS

Edited by N. J. A. Sloane, Jul 06 2009

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 25 15:25 EDT 2018. Contains 315392 sequences. (Running on oeis4.)