%I #16 Feb 16 2025 08:33:29

%S 1,2,2,4,5,8,5,12,5,16,5,20,5,24,5,28,5,32,5,36,5,40,5,44,5,48,5,52,5,

%T 56,5,60,5,64,5,68,5,72,5,76,5,80,5,84,5,88,5,92,5,96,5,100,5,104,5,

%U 108,5,112,5,116,5,120,5,124,5,128,5,132,5,136,5,140

%N Number of ON (black) cells in the n-th iteration of the "Rule 91" 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="/A267046/b267046.txt">Table of n, a(n) for n = 0..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="https://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 10 2016 and Apr 19 2019: (Start)

%F a(n) = 3/2+(7*(-1)^n)/2+n-(-1)^n*n for n>2.

%F a(n) = 2*a(n-2)-a(n-4) for n>6.

%F G.f.: (1+2*x+2*x^4+2*x^5-3*x^6) / ((1-x)^2*(1+x)^2).

%F (End)

%t rule=91; 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. A267015.

%K nonn,easy

%O 0,2

%A _Robert Price_, Jan 09 2016