A269522 - OEIS

%I #15 Mar 01 2016 22:55:03

%S 1,5,9,21,25,37,57,69,89,101,121,133,169,205,257,309,361,333,377,381,

%T 385,461,465,509,601,653,697,781,889,845,1097,1077,1353,1205,1305,

%U 1349,1345,1357,1321,1437,1553,1589,1601,1709,1729,1813,1937,2069,2361,2181

%N Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 622", based on the 5-celled von Neumann neighborhood.

%C Initialized with a single black (ON) cell at stage zero.

%D S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.

%H Robert Price, <a href="/A269522/b269522.txt">Table of n, a(n) for n = 0..300</a>

%H Robert Price, <a href="/A269522/a269522.tmp.txt">Diagrams of first 20 stages</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, 2015

%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_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>

%H <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>

%t rule=622; stages=300; ca=CellularAutomaton[ {rule,{2,{{0,2,0},{2,1,2},{0,2,0}}},{1,1}}, {{{1}},0}, stages]; (* Start with single black cell *) Map[Function[Apply[Plus,Flatten[#1]]],ca] (* Count ON cells at each stage *)

%Y Cf. A007483, A072272, A170878, A253908.

%K nonn,easy

%O 0,2

%A _Robert Price_, Feb 28 2016