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%I #20 Apr 16 2019 15:24:39
%S 1,0,1,4,1,8,1,12,1,16,1,20,1,24,1,28,1,32,1,36,1,40,1,44,1,48,1,52,1,
%T 56,1,60,1,64,1,68,1,72,1,76,1,80,1,84,1,88,1,92,1,96,1,100,1,104,1,
%U 108,1,112,1,116,1,120,1,124,1,128,1,132,1,136,1,140
%N Number of ON (black) cells in the n-th iteration of the "Rule 1" elementary cellular automaton starting with a single ON (black) cell.
%D S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H Colin Barker, <a href="/A265722/b265722.txt">Table of n, a(n) for n = 0..1000</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 Conjectures from _Colin Barker_, Dec 14 2015 and Apr 16 2019: (Start)
%F a(n) = 1/2*(-2*(-1)^n*n+2*n+3*(-1)^n-1).
%F a(n) = 2*a(n-2) - a(n-4) for n>3.
%F G.f.: (1-x^2+4*x^3) / ((1-x)^2*(1+x)^2).
%F (End)
%F a(n) = A019425(n), n>1. - _R. J. Mathar_, Jan 10 2016
%e From _Michael De Vlieger_, Dec 14 2015: (Start)
%e First 12 rows, replacing zeros with "." for better visibility of ON cells, followed by the total number of 1's per row at right:
%e 1 = 1
%e . . . = 0
%e . . 1 . . = 1
%e 1 1 . . . 1 1 = 4
%e . . . . 1 . . . . = 1
%e 1 1 1 1 . . . 1 1 1 1 = 8
%e . . . . . . 1 . . . . . . = 1
%e 1 1 1 1 1 1 . . . 1 1 1 1 1 1 = 12
%e . . . . . . . . 1 . . . . . . . . = 1
%e 1 1 1 1 1 1 1 1 . . . 1 1 1 1 1 1 1 1 = 16
%e . . . . . . . . . . 1 . . . . . . . . . . = 1
%e 1 1 1 1 1 1 1 1 1 1 . . . 1 1 1 1 1 1 1 1 1 1 = 20
%e (End)
%t rule = 1; rows = 30; Table[Total[Table[Take[CellularAutomaton[rule, {{1},0},rows-1,{All,All}][[k]], {rows-k+1, rows+k-1}], {k,1,rows}][[k]]], {k,1,rows}]
%Y Cf. A265718, A265720, A265721.
%K nonn,easy
%O 0,4
%A _Robert Price_, Dec 14 2015