|
%I #16 Apr 17 2019 08:58:46
%S 0,2,6,8,16,18,30,32,48,50,70,72,96,98,126,128,160,162,198,200,240,
%T 242,286,288,336,338,390,392,448,450,510,512,576,578,646,648,720,722,
%U 798,800,880,882,966,968,1056,1058,1150,1152,1248,1250,1350,1352,1456
%N Total number of OFF (white) cells after n iterations of the "Rule 3" elementary cellular automaton starting with a single ON (black) cell.
%D S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H Robert Price, <a href="/A266074/b266074.txt">Table of n, a(n) for n = 0..999</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%F Empirical g.f.: (2*(-x - 2*x^2 + x^3))/((-1 + x)^3*(1 + x)^2). - _Michael De Vlieger_, Dec 21 2015
%F Empirical a(n) = 1/4*(2*n^2 + 2*(-1)^n*n + 6*n - (-1)^n + 1). - _Colin Barker_, Dec 21 2015
%F a(n) = 2*A135276(n). - _Alois P. Heinz_, Dec 21 2015
%e From _Michael De Vlieger_, Dec 21 2015: (Start)
%e First 12 rows, replacing "1" with "." for better visibility of OFF cells, followed by the total number of 0's per row, then the running total up to and including that row:
%e . = 0 -> 0
%e . 0 0 = 2 -> 2
%e 0 0 0 . 0 = 4 -> 6
%e . . . . 0 0 . = 2 -> 8
%e 0 0 0 0 0 0 . 0 0 = 8 -> 16
%e . . . . . . . 0 0 . . = 2 -> 18
%e 0 0 0 0 0 0 0 0 0 . 0 0 0 = 12 -> 30
%e . . . . . . . . . . 0 0 . . . = 2 -> 32
%e 0 0 0 0 0 0 0 0 0 0 0 0 . 0 0 0 0 = 16 -> 48
%e . . . . . . . . . . . . . 0 0 . . . . = 2 -> 50
%e 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 . 0 0 0 0 0 = 20 -> 70
%e . . . . . . . . . . . . . . . . 0 0 . . . . . = 2 -> 72
%e (End)
%Y Cf. A135276.
%K nonn,easy
%O 0,2
%A _Robert Price_, Dec 20 2015
|
