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

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A094374 a(n)=(3^n-1)/2+2^n. 3
1, 3, 8, 21, 56, 153, 428, 1221, 3536, 10353, 30548, 90621, 269816, 805353, 2407868, 7207221, 21588896, 64701153, 193972388, 581655021, 1744440776, 5232273753, 15694724108, 47079978021, 141231545456, 423677859153, 1271000023028 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A094373.

Row sums of A125103. - Paul Barry, Dec 04 2007

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 disjoint and for which x is not a subset of y and y is not a subset of x, or 2) x = y. - Ross La Haye, Jan 11 2008

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

A. Prasad, Equivalence classes of nodes in trees and rational generating functions, arXiv preprint arXiv:1407.5284, 2014

LINKS

Table of n, a(n) for n=0..26.

Index to sequences with linear recurrences with constant coefficients, signature (6,-11,6).

FORMULA

G.f.: (1-3x+x^2)/((1-x)(1-2x)(1-3x)); a(n)=6a(n-1)-11a(n-2)+6a(n-3). a(n)=A003462(n)+A000079(n).

a(n)=sum{k=0..n, C(n,k)+2^k*C(n,k+1)}; - Paul Barry, Dec 04 2007

a(n) = StirlingS2(n+1,3) + 2*StirlingS2(n+1,2) + 1. - Ross La Haye, Jan 11 2008

a(0)=1, a(1)=3, a(2)=8, a(n)=6*a(n-1)-11*a(n-2)+6*a(n-3). - Harvey P. Dale, Jul 22 2013

MATHEMATICA

Table[(3^n-1)/2+2^n, {n, 0, 30}] (* or *) LinearRecurrence[{6, -11, 6}, {1, 3, 8}, 30] (* Harvey P. Dale, Jul 22 2013 *)

CROSSREFS

Cf. A000225, A000392, A000079.

Sequence in context: A128105 A085560 A243633 * A008909 A006835 A014318

Adjacent sequences:  A094371 A094372 A094373 * A094375 A094376 A094377

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Apr 28 2004

STATUS

approved

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

Content is available under The OEIS End-User License Agreement .

Last modified December 22 04:20 EST 2014. Contains 252328 sequences.