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A056182 First differences of A003063. 8
0, 2, 10, 38, 130, 422, 1330, 4118, 12610, 38342, 116050, 350198, 1054690, 3172262, 9533170, 28632278, 85962370, 258018182, 774316690, 2323474358, 6971471650, 20916512102, 62753730610, 188269580438, 564825518530 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Let V be a binary relation on the power set P(A) of a set A having n = |A| elements such that for every element x, y of P(A), xVy if x is a proper subset of y or y is a proper subset of x. Then a(n) = |V|. - Ross La Haye, Dec 22 2006

It appears that a(n) is the number of permutations p of 1,..,(n+2) such that max[p(i+1)-p(i)] is 2.  For example, for n=1, the permutations (1,3,2) and (2,1,3) and no others have the desired property, so a(1)=2.  This approach gives values in agreement with all listed terms. [John W. Layman, Nov 09 2011]

LINKS

Vincenzo Librandi, 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.

Index entries for linear recurrences with constant coefficients, signature (5,-6).

FORMULA

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

a(n) = 5*a(n-1)-6*a(n-2). G.f.: 2*x/((2*x-1)*(3*x-1)). [Colin Barker, Dec 10 2012]

a(n) = A217764(n,3). - Ross La Haye, Mar 27 2013

a(n) = sum_{i=1..n} binomial(n, i) * 2^(n - i + 1). - Wesley Ivan Hurt, Feb 10 2014

a(n) = 2 * A001047(n). - Wesley Ivan Hurt, Feb 10 2014

MAPLE

A056182:=n->2 * (3^n - 2^n); seq(A056182(n), n=0..30); # Wesley Ivan Hurt, Feb 10 2014

MATHEMATICA

Table[ -((-1 + k)^(1-k+n)*(-1+k)!)+k^(-k+n)*k! /. k -> 3, {n, 3, 36} ]

Table[2 (3^n - 2^n), {n, 0, 30}] (* Wesley Ivan Hurt, Feb 10 2014 *)

CoefficientList[Series[2 x/((2 x - 1) (3 x - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Feb 12 2014 *)

LinearRecurrence[{5, -6}, {0, 2}, 30] (* Harvey P. Dale, Sep 22 2015 *)

CROSSREFS

3rd column of A056151.

A002783(n) - 1.

a(n) = A293181(n+1,3).

Sequence in context: A119358 A110148 A281199 * A081956 A120278 A166898

Adjacent sequences:  A056179 A056180 A056181 * A056183 A056184 A056185

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Aug 05 2000

EXTENSIONS

More terms from Wouter Meeussen, Aug 05 2000

STATUS

approved

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Last modified September 20 05:51 EDT 2019. Contains 327212 sequences. (Running on oeis4.)