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%I #19 Feb 24 2021 02:48:19
%S 0,1,5,9,21,29,41,53,89,117,129,141,177,205,241,277,385,485,497,509,
%T 545,573,609,645,753,845,881,917,1025,1109,1217,1325,1649,1989,2001,
%U 2013,2049,2077,2113,2149,2257,2349,2385,2421,2529,2613,2721,2829
%N Total number of cells that are ON at stage n in Wolfram's 2-D cellular automaton defined by Rule 942.
%C We work on the square grid. A cell is turned ON iff exactly one or four of its four neighbors is ON. Once a cell is ON it stays ON. At stage -1 all cells are OFF. At stage 0 a single cell is turned ON.
%D S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 928.
%H N. J. A. Sloane, <a href="/A169649/b169649.txt">Table of n, a(n) for n = -1..549</a>
%H David Applegate, <a href="/A139250/a139250.anim.html">The movie version</a>
%H David Applegate, Omar E. Pol and N. J. A. Sloane, <a href="/A000695/a000695_1.pdf">The Toothpick Sequence and Other Sequences from Cellular Automata</a>, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]
%H N. J. A. Sloane, <a href="/A169649/a169649.png">Illustration of first 24 generations (png)</a>
%H N. J. A. Sloane, <a href="/A169649/a169649.pdf">Illustration of first 24 generations (pdf)</a>
%H N. J. A. Sloane, <a href="/wiki/Catalog_of_Toothpick_and_CA_Sequences_in_OEIS">Catalog of Toothpick and Cellular Automata Sequences in the OEIS</a>
%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%t Map[Function[Apply[Plus, Flatten[ #1]]], CellularAutomaton[{ 942, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, 100]]
%t ArrayPlot /@ CellularAutomaton[{942, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, 23]
%Y Partial sums of A169648.
%K nonn
%O -1,3
%A _N. J. A. Sloane_, Apr 07 2010
%E Added Mma programs and illustrations. - _N. J. A. Sloane_, Sep 21 2014
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