A267458 - OEIS

%I #23 Apr 19 2019 14:47:57

%S 1,1,1,1,3,3,5,5,7,7,9,9,11,11,13,13,15,15,17,17,19,19,21,21,23,23,25,

%T 25,27,27,29,29,31,31,33,33,35,35,37,37,39,39,41,41,43,43,45,45,47,47,

%U 49,49,51,51,53,53,55,55,57,57,59,59,61,61,63,63,65,65

%N Number of ON (black) cells in the n-th iteration of the "Rule 133" elementary cellular automaton starting with a single ON (black) cell.

%C 1,1, followed by A109613 (odd integers repeated).

%D S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

%H Robert Price, <a href="/A267458/b267458.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 a(n) = A109613(n-2) for n>=2.

%F Conjectures from _Colin Barker_, Jan 15 2016 and Apr 19 2019: (Start)

%F a(n) = (2*n+(-1)^n-3)/2 for n>1.

%F a(n) = a(n-1)+a(n-2)-a(n-3) for n>4.

%F G.f.: (1-x^2+2*x^4) / ((1-x)^2*(1+x)).

%F (End)

%t rule=133; 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. A267423.

%K nonn,easy

%O 0,5

%A _Robert Price_, Jan 15 2016