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A266074 Total number of OFF (white) cells after n iterations of the "Rule 3" elementary cellular automaton starting with a single ON (black) cell.

%I A266074 #17 Feb 16 2025 08:33:28
%S A266074 0,2,6,8,16,18,30,32,48,50,70,72,96,98,126,128,160,162,198,200,240,
%T A266074 242,286,288,336,338,390,392,448,450,510,512,576,578,646,648,720,722,
%U A266074 798,800,880,882,966,968,1056,1058,1150,1152,1248,1250,1350,1352,1456
%N A266074 Total number of OFF (white) cells after n iterations of the "Rule 3" elementary cellular automaton starting with a single ON (black) cell.
%D A266074 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H A266074 Robert Price, <a href="/A266074/b266074.txt">Table of n, a(n) for n = 0..999</a>
%H A266074 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A266074 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A266074 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%F A266074 Empirical g.f.: (2*(-x - 2*x^2 + x^3))/((-1 + x)^3*(1 + x)^2). - _Michael De Vlieger_, Dec 21 2015
%F A266074 Empirical a(n) = 1/4*(2*n^2 + 2*(-1)^n*n + 6*n - (-1)^n + 1). - _Colin Barker_, Dec 21 2015
%F A266074 a(n) = 2*A135276(n). - _Alois P. Heinz_, Dec 21 2015
%e A266074 From _Michael De Vlieger_, Dec 21 2015: (Start)
%e A266074 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 A266074                       .                        =  0  ->  0
%e A266074                     . 0 0                      =  2  ->  2
%e A266074                   0 0 0 . 0                    =  4  ->  6
%e A266074                 . . . . 0 0 .                  =  2  ->  8
%e A266074               0 0 0 0 0 0 . 0 0                =  8  -> 16
%e A266074             . . . . . . . 0 0 . .              =  2  -> 18
%e A266074           0 0 0 0 0 0 0 0 0 . 0 0 0            = 12  -> 30
%e A266074         . . . . . . . . . . 0 0 . . .          =  2  -> 32
%e A266074       0 0 0 0 0 0 0 0 0 0 0 0 . 0 0 0 0        = 16  -> 48
%e A266074     . . . . . . . . . . . . . 0 0 . . . .      =  2  -> 50
%e A266074   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 . 0 0 0 0 0    = 20  -> 70
%e A266074 . . . . . . . . . . . . . . . . 0 0 . . . . .  =  2  -> 72
%e A266074 (End)
%Y A266074 Cf. A135276.
%K A266074 nonn,easy
%O A266074 0,2
%A A266074 _Robert Price_, Dec 20 2015