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A266073 Number of OFF (white) cells in the n-th iteration of the "Rule 3" elementary cellular automaton starting with a single ON (black) cell.

%I A266073 #17 Feb 16 2025 08:33:28
%S A266073 0,2,4,2,8,2,12,2,16,2,20,2,24,2,28,2,32,2,36,2,40,2,44,2,48,2,52,2,
%T A266073 56,2,60,2,64,2,68,2,72,2,76,2,80,2,84,2,88,2,92,2,96,2,100,2,104,2,
%U A266073 108,2,112,2,116,2,120,2,124,2,128,2,132,2,136,2,140,2
%N A266073 Number of OFF (white) cells in the n-th iteration of the "Rule 3" elementary cellular automaton starting with a single ON (black) cell.
%D A266073 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H A266073 Robert Price, <a href="/A266073/b266073.txt">Table of n, a(n) for n = 0..999</a>
%H A266073 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A266073 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A266073 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%F A266073 Empirical g.f.: (-2*(-x - 2*x^2 + x^3))/(-1 + x^2)^2. - _Michael De Vlieger_, Dec 21 2015
%F A266073 Conjectures from _Colin Barker_, Dec 21 2015 and Apr 17 2019: (Start)
%F A266073 a(n) = (-1)^n*n+n-(-1)^n+1.
%F A266073 a(n) = 2*a(n-2) - a(n-4) for n>3.
%F A266073 (End)
%e A266073 From _Michael De Vlieger_, Dec 21 2015: (Start)
%e A266073 First 12 rows, replacing "0" with "." for better visibility of OFF cells, followed by the total number of 0's per row:
%e A266073                       .                        =  0
%e A266073                     . 0 0                      =  2
%e A266073                   0 0 0 . 0                    =  4
%e A266073                 . . . . 0 0 .                  =  2
%e A266073               0 0 0 0 0 0 . 0 0                =  8
%e A266073             . . . . . . . 0 0 . .              =  2
%e A266073           0 0 0 0 0 0 0 0 0 . 0 0 0            = 12
%e A266073         . . . . . . . . . . 0 0 . . .          =  2
%e A266073       0 0 0 0 0 0 0 0 0 0 0 0 . 0 0 0 0        = 16
%e A266073     . . . . . . . . . . . . . 0 0 . . . .      =  2
%e A266073   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 . 0 0 0 0 0    = 20
%e A266073 . . . . . . . . . . . . . . . . 0 0 . . . . .  =  2
%e A266073 (End)
%K A266073 nonn,easy
%O A266073 0,2
%A A266073 _Robert Price_, Dec 20 2015