login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A094033 Number of connected 2-element antichains on a labeled n-set. 16
0, 0, 0, 3, 18, 75, 270, 903, 2898, 9075, 27990, 85503, 259578, 784875, 2366910, 7125303, 21425058, 64373475, 193317030, 580344303, 1741819338, 5227030875, 15684238350, 47059006503, 141189602418, 423593973075, 1270832250870 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

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. - Ross La Haye, Jan 10 2008

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

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.

Adam Roman, Igor T. Podolak and Agnieszka Deszynska, On the number of clusterings in a hierarchical classification model with overlapping clusters, Schedae Informaticae, Volume 20, 2011.

FORMULA

a(n) = 3 * A000392(n).

E.g.f.: (exp(3*x)-3*exp(2*x)+3*exp(x)-1)/2!.

From Colin Barker, Mar 31 2012: (Start)

a(n) = (3^n-3*2^n+3)/2.

a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3).

G.f.: 3*x^3/((1-x)*(1-2*x)*(1-3*x)). (End)

MAPLE

[seq(stirling2(n, 3)*3, n=0..26)]; # Zerinvary Lajos, Dec 06 2006

MATHEMATICA

Table[3 StirlingS2[n, 3], {n, 0, 26}] (* Michael De Vlieger, Nov 30 2015 *)

PROG

(PARI) x='x+O('x^50); concat([0, 0, 0], Vec(serlaplace((exp(3*x)-3*exp(2*x)+3*exp(x)-1)/2!))) \\ G. C. Greubel, Oct 06 2017

CROSSREFS

Cf. A016269, A047707.

Cf. A051112, A051113, A051114, A051115, A051116, A051117, A051118.

Cf. A094034, A094035, A094036, A094037.

Sequence in context: A152897 A059393 A301820 * A245580 A043008 A241628

Adjacent sequences:  A094030 A094031 A094032 * A094034 A094035 A094036

KEYWORD

nonn

AUTHOR

Goran Kilibarda, Vladeta Jovovic, Apr 22 2004

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 23 14:42 EDT 2021. Contains 348214 sequences. (Running on oeis4.)