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A100774 a(n) = 2*(3^n - 1). 13
0, 4, 16, 52, 160, 484, 1456, 4372, 13120, 39364, 118096, 354292, 1062880, 3188644, 9565936, 28697812, 86093440, 258280324, 774840976, 2324522932, 6973568800, 20920706404, 62762119216, 188286357652, 564859072960, 1694577218884 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) is the number of steps which are made when generating all n-step nonreversing random walks that begin in a fixed point P on a two-dimensional square lattice. To make one step means to move along one edge on the lattice.

These are also the first local maxima reached in the Collatz trajectories of 2^n - 1. - David Rabahy, Oct 30 2017

Also the graph diameter of the n-Sierpinski carpet graph. - Eric W. Weisstein, Mar 13 2018

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..196

Eric Weisstein's World of Mathematics, Graph Diameter

Eric Weisstein's World of Mathematics, Sierpinski Carpet Graph

Index entries for linear recurrences with constant coefficients, signature (-4, -3).

FORMULA

a(n) = 2*(3^n - 1);

a(0) = 0, a(n) = 4*Sum_{i = 0 to n - 1} 3^i for n > 0;

a(n) = 4*A003462(n).

a(n) = A048473(n) - 1. - Paul Curtz, Jan 19 2009

G.f.: 4 x/(1 - 4 x + 3 x^2). - Eric W. Weisstein, Mar 13 2018

a(n) = 4*a(n-1) - 3*a(n-2). - Eric W. Weisstein, Mar 13 2018

MATHEMATICA

Table[2 (3^n - 1), {n, 0, 24}] (* Alonso del Arte, Nov 08 2012 *)

2 (3^Range[0, 20] - 1) (* Eric W. Weisstein, Mar 13 2018 *)

LinearRecurrence[{4, -3}, {4, 16}, {0, 20}] (* Eric W. Weisstein, Mar 13 2018 *)

CoefficientList[Series[4 x/(1 - 4 x + 3 x^2), {x, 0, 20}], x] (* Eric W. Weisstein, Mar 13 2018 *)

PROG

(MAGMA) [2*(3^n - 1): n in [0..25] ]; // Vincenzo Librandi, Apr 30 2011

(Maxima) A100774(n):=2*(3^n - 1)$

makelist(A100774(n), n, 0, 30); /* Martin Ettl, Nov 09 2012 */

(PARI) a(n)=2*3^n-2 \\ Charles R Greathouse IV, Nov 09 2012

CROSSREFS

Cf. A003462, A007051, A034472, A024023, A067771, A029858, A134931, A115099, A100774, A079004, A058481.

Sequence in context: A320237 A197132 A266943 * A336994 A107767 A319775

Adjacent sequences:  A100771 A100772 A100773 * A100775 A100776 A100777

KEYWORD

easy,nonn

AUTHOR

Pawel P. Mazur (Pawel.Mazur(AT)pwr.wroc.pl), Apr 06 2005

STATUS

approved

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Last modified August 9 18:55 EDT 2022. Contains 356026 sequences. (Running on oeis4.)