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A056182 First differences of A003063. 10
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]

In the terdragon curve, a(n-1) is the number of enclosed unit triangles in expansion level n. - Kevin Ryde, Oct 20 2020

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.

Kevin Ryde, Iterations of the Terdragon Curve, see index "A area".

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.  Cf. A028243 (partial sums).

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 May 12 03:08 EDT 2021. Contains 343810 sequences. (Running on oeis4.)