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A164982 Number of ON cells after n generations of the 2D cellular automaton described in the comments.

%I A164982 #13 Jul 13 2022 12:59:16
%S A164982 1,3,4,12,7,21,16,40,22,42,34,67,52,85,70,125,94,126,102,150,118,172,
%T A164982 177,234,209,240,238,319,285,363,378,458,383,444,404,493,474,520,529,
%U A164982 628,583,602,622,727,664,816,835,948,873,926,952,1065,1010,1090,1187
%N A164982 Number of ON cells after n generations of the 2D cellular automaton described in the comments.
%C A164982 The cells are the squares of the standard square grid. All cells are initially OFF and one cell is turned ON at generation 1. At subsequent generations a cell is ON if and only if (1) exactly one of neighbors NW, NE, and S was ON, or (2) all three of cells N, SW, and SE were ON in the previous generation. (The 9-cell Moore neighborhood is labeled {{NW,N,NE},{W,C,E},{SW,S,SE}}).
%H A164982 John W. Layman, <a href="https://personal.math.vt.edu/layman/sequences/A164982.htm">Graphs of the automaton for generations 1-20</a> [From _John W. Layman_, Sep 14 2009]
%H A164982 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%t A164982 RasterGraphics[state_?MatrixQ, colors_Integer : 2, opts___] := Graphics[Raster[Reverse[1 - state/(colors - 1)]], AspectRatio -> (AspectRatio /. {opts} /. AspectRatio -> Automatic), Frame -> True, FrameTicks -> None, GridLines -> None];
%t A164982 rule=61986;
%t A164982 Show[GraphicsArray[Map[RasterGraphics, CellularAutomaton[{rule, {2, {{1, 4, 1}, {0, 0, 0}, {4, 1, 4}}}, {1, 1}}, {{{1}}, 0}, 4, -5]]]];
%t A164982 ca = CellularAutomaton[{rule, {2, {{1, 4, 1}, {0, 0, 0}, {4, 1, 4}}}, {1, 1}}, {{{1}}, 0}, 99, -100];
%t A164982 Table[Total[ca[[i]], 2], {i, 1, 100}]
%Y A164982 Cf. A048883, A072272, A122108, A160410, A247002.
%K A164982 nonn
%O A164982 1,2
%A A164982 _John W. Layman_, Sep 03 2009