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A267049 Total number of OFF (white) cells after n iterations of the "Rule 91" elementary cellular automaton starting with a single ON (black) cell. 1

%I #17 Apr 19 2019 05:13:09

%S 0,1,4,7,11,14,22,25,37,40,56,59,79,82,106,109,137,140,172,175,211,

%T 214,254,257,301,304,352,355,407,410,466,469,529,532,596,599,667,670,

%U 742,745,821,824,904,907,991,994,1082,1085,1177,1180,1276,1279,1379,1382

%N Total number of OFF (white) cells after n iterations 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="/A267049/b267049.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 11 2016 and Apr 19 2019: (Start)

%F a(n) = (n^2+(-1)^n*(n-3)+5)/2 for n>1.

%F a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5) for n>6.

%F G.f.: x*(1+3*x+x^2-2*x^3-2*x^4+3*x^5) / ((1-x)^3*(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 *) nbc=Table[Total[catri[[k]]],{k,1,rows}]; (* Number of Black cells in stage n *) nwc=Table[Length[catri[[k]]]-nbc[[k]],{k,1,rows}]; (* Number of White cells in stage n *) Table[Total[Take[nwc,k]],{k,1,rows}] (* Number of White cells through stage n *)

%Y Cf. A267015.

%K nonn

%O 0,3

%A _Robert Price_, Jan 09 2016

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)