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A255298 Number of ON cells after n generations of the odd-rule cellular automaton defined by OddRule 143 when started with a single ON cell. 2

%I #17 Sep 30 2016 13:09:10

%S 1,4,4,16,4,16,16,58,4,16,16,64,16,64,58,204,4,16,16,64,16,64,64,232,

%T 16,64,64,256,58,232,204,714,4,16,16,64,16,64,64,232,16,64,64,256,64,

%U 256,232,816,16,64,64,256,64,256,256,928,58,232,232,928,204

%N Number of ON cells after n generations of the odd-rule cellular automaton defined by OddRule 143 when started with a single ON cell.

%H JungHwan Min, <a href="/A255298/b255298.txt">Table of n, a(n) for n = 0..10000</a>

%H Shalosh B. Ekhad, N. J. A. Sloane, and Doron Zeilberger, <a href="http://arxiv.org/abs/1503.01796">A Meta-Algorithm for Creating Fast Algorithms for Counting ON Cells in Odd-Rule Cellular Automata</a>, arXiv:1503.01796 [math.CO], 2015; see also the <a href="http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/CAcount.html">Accompanying Maple Package</a>.

%H Shalosh B. Ekhad, N. J. A. Sloane, and Doron Zeilberger, <a href="http://arxiv.org/abs/1503.04249">Odd-Rule Cellular Automata on the Square Grid</a>, arXiv:1503.04249 [math.CO], 2015.

%H N. J. A. Sloane, On the No. of ON Cells in Cellular Automata, Video of talk in Doron Zeilberger's Experimental Math Seminar at Rutgers University, Feb. 05 2015: <a href="https://vimeo.com/119073818">Part 1</a>, <a href="https://vimeo.com/119073819">Part 2</a>

%H N. J. A. Sloane, <a href="http://arxiv.org/abs/1503.01168">On the Number of ON Cells in Cellular Automata</a>, arXiv:1503.01168 [math.CO], 2015.

%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>

%t A255298[n_] := Total[CellularAutomaton[{10, {2, {{0, 0, 1}, {1, 0, 0}, {0, 1, 1}}}, {1, 1}}, {{{1}}, 0}, {{{n}}}], 2]; Array[A255298, 61, 0] (* _JungHwan Min_, Sep 29 2016 *)

%t A255298L[n_] := Total[#, 2] & /@ CellularAutomaton[{10, {2, {{0, 0, 1}, {1, 0, 0}, {0, 1, 1}}}, {1, 1}}, {{{1}}, 0}, n]; A255298L[60] (* _JungHwan Min_, Sep 29 2016 *)

%Y Run length transform of A255299.

%K nonn

%O 0,2

%A _N. J. A. Sloane_ and _Doron Zeilberger_, Feb 23 2015

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Last modified March 28 12:26 EDT 2024. Contains 371254 sequences. (Running on oeis4.)