A266303 - OEIS

%I #17 Apr 15 2019 06:02:03

%S 1,2,1,6,1,10,1,14,1,18,1,22,1,26,1,30,1,34,1,38,1,42,1,46,1,50,1,54,

%T 1,58,1,62,1,66,1,70,1,74,1,78,1,82,1,86,1,90,1,94,1,98,1,102,1,106,1,

%U 110,1,114,1,118,1,122,1,126,1,130,1,134,1,138,1

%N Number of ON (black) cells in the n-th iteration of the "Rule 15" 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="/A266303/b266303.txt">Table of n, a(n) for n = 0..999</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 28 2015 and Apr 15 2019: (Start)

%F a(n) = (1+(-1)^n-2*(-1+(-1)^n)*n)/2.

%F a(n) = 2*a(n-2)-a(n-4) for n>3.

%F G.f.: (1+2*x-x^2+2*x^3) / ((1-x)^2*(1+x)^2).

%F (End)

%t rule=15; 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 *) Table[Total[catri[[k]]],{k,1,rows}] (* Number of Black cells in stage n *)

%Y Cf. A266300.

%K nonn,easy

%O 0,2

%A _Robert Price_, Dec 26 2015