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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 - x)*(1 - 3*x)). - 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, A048473. 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 September 25 16:39 EDT 2023. Contains 365648 sequences. (Running on oeis4.)