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A265223 Total number of OFF (white) cells after n iterations of the "Rule 150" elementary cellular automaton starting with a single ON (black) cell.

%I A265223 #26 Feb 16 2025 08:33:27
%S A265223 0,0,2,4,10,12,20,24,38,48,60,68,88,100,118,128,158,184,212,236,268,
%T A265223 284,314,328,372,408,446,476,522,548,588,608,670,728,788,844,908,956,
%U A265223 1018,1064,1136,1192,1250,1292,1366,1412,1472,1504,1596,1680,1766,1844
%N A265223 Total number of OFF (white) cells after n iterations of the "Rule 150" elementary cellular automaton starting with a single ON (black) cell.
%D A265223 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H A265223 Robert Price, <a href="/A265223/b265223.txt">Table of n, a(n) for n = 0..999</a>
%H A265223 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A265223 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A265223 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%e A265223 From _Michael De Vlieger_, Dec 09 2015: (Start)
%e A265223 First 12 rows, replacing "1" with ".", ignoring "0" outside of range of 1's for better visibility of OFF cells, followed by total number of OFF cells per row and running total up to that row:
%e A265223                         .                          =  0 ->   0
%e A265223                       . . .                        =  0 ->   0
%e A265223                     . 0 . 0 .                      =  2 ->   2
%e A265223                   . . 0 . 0 . .                    =  2 ->   4
%e A265223                 . 0 0 0 . 0 0 0 .                  =  6 ->  10
%e A265223               . . . 0 . . . 0 . . .                =  2 ->  12
%e A265223             . 0 . 0 0 0 . 0 0 0 . 0 .              =  8 ->  20
%e A265223           . . 0 . . 0 . . . 0 . . 0 . .            =  4 ->  24
%e A265223         . 0 0 0 0 0 0 0 . 0 0 0 0 0 0 0 .          = 14 ->  38
%e A265223       . . . 0 0 0 0 0 . . . 0 0 0 0 0 . . .        = 10 ->  48
%e A265223     . 0 . 0 . 0 0 0 . 0 . 0 . 0 0 0 . 0 . 0 .      = 12 ->  60
%e A265223   . . 0 . 0 . . 0 . . 0 . 0 . . 0 . . 0 . 0 . .    =  8 ->  68
%e A265223 . 0 0 0 . 0 0 0 0 0 0 0 . 0 0 0 0 0 0 0 . 0 0 0 .  = 20 ->  88
%e A265223 (End)
%t A265223 lim = 51; a = {}; Do[AppendTo[a, Take[#, 2 (k - 1) + 1] &@ Take[#[[k]], -(lim + k)]], {k, Length@ #}] &@ CellularAutomaton[150, {{1}, 0}, lim]; Accumulate[Count[#, n_ /; n == 0] & /@ a] (* _Michael De Vlieger_, Dec 09 2015 *)
%Y A265223 Cf. A071036.
%K A265223 nonn,easy
%O A265223 0,3
%A A265223 _Robert Price_, Dec 07 2015