%I #16 Apr 18 2019 09:46:06
%S 0,2,2,5,6,5,10,5,14,5,18,5,22,5,26,5,30,5,34,5,38,5,42,5,46,5,50,5,
%T 54,5,58,5,62,5,66,5,70,5,74,5,78,5,82,5,86,5,90,5,94,5,98,5,102,5,
%U 106,5,110,5,114,5,118,5,122,5,126,5,130,5,134,5,138,5
%N Number of OFF (white) cells in the n-th iteration of the "Rule 37" 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="/A266595/b266595.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 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</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_, Jan 02 2016 and Apr 18 2019: (Start)
%F a(n) = (2*(-1)^n*n+2*n-7*(-1)^n+3)/2 for n>1.
%F a(n) = 2*a(n-2)-a(n-4) for n>4.
%F G.f.: x*(2+2*x+x^2+2*x^3-3*x^4) / ((1-x)^2*(1+x)^2).
%F (End)
%t rule=37; rows=20; ca=CellularAutomaton[rule,{{1},0},rows-1,{All,All}]; (* Start with single black cell *) catri=Table[Take[ca[[k]],{rows-k+1,rows+k-1}],{k,1,rows}]; (* Truncated list of each row *) nbc=Table[Total[catri[[k]]],{k,1,rows}]; (* Number of Black cells in stage n *) Table[Length[catri[[k]]]-nbc[[k]],{k,1,rows}] (* Number of White cells in stage n *)
%Y Cf. A266588.
%K nonn,easy
%O 0,2
%A _Robert Price_, Jan 01 2016