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A350632 a(n) is the total number of ON cells at stage n of a cellular automaton where cells are turned ON when they have one or two neighbors ON (see Comments for precise definition).

%I A350632 #16 Jan 22 2022 08:38:54
%S A350632 0,1,9,21,45,57,85,121,177,189,217,253,329,373,465,557,721,737,765,
%T A350632 801,877,921,1013,1105,1301,1377,1485,1601,1805,1985,2221,2449,2873,
%U A350632 2909,2937,2973,3049,3093,3185,3277,3473,3549,3657,3773,3977,4157,4393,4621,5113
%N A350632 a(n) is the total number of ON cells at stage n of a cellular automaton where cells are turned ON when they have one or two neighbors ON (see Comments for precise definition).
%C A350632 On the infinite square grid, start with all cells OFF.
%C A350632 Turn a single cell to the ON state.
%C A350632 At each subsequent step, each cell with exactly one or two neighbors ON is turned ON, and everything that is already ON remains ON.
%C A350632 Here "neighbor" refers to the eight adjacent and diagonally adjacent cells in the Moore neighborhood.
%H A350632 Rémy Sigrist, <a href="/A350632/a350632.png">Log periodic coloring of the structure at stage 512</a>
%H A350632 Rémy Sigrist, <a href="/A350632/a350632_1.txt">C++ program for A350632</a>
%H A350632 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%e A350632 The first 5 generations can be depicted as follows:
%e A350632          . . . . . . . . . . .
%e A350632          . 5 5 . . . . . 5 5 .
%e A350632          . 5 4 4 4 4 4 4 4 5 .
%e A350632          . . 4 3 3 . 3 3 4 . .
%e A350632          . . 4 3 2 2 2 3 4 . .
%e A350632          . . 4 . 2 1 2 . 4 . .
%e A350632          . . 4 3 2 2 2 3 4 . .
%e A350632          . . 4 3 3 . 3 3 4 . .
%e A350632          . 5 4 4 4 4 4 4 4 5 .
%e A350632          . 5 5 . . . . . 5 5 .
%e A350632          . . . . . . . . . . .
%e A350632 - so a(0) = 0,
%e A350632      a(1) = 0 + 1 = 1,
%e A350632      a(2) = 1 + 8 = 9,
%e A350632      a(3) = 9 + 12 = 21,
%e A350632      a(4) = 21 + 24 = 45,
%e A350632      a(5) = 45 + 12 = 57.
%o A350632 (C++) See Links section.
%Y A350632 Cf. A147562, A151725, A160414, A256530, A350633, A350639.
%K A350632 nonn
%O A350632 0,3
%A A350632 _Rémy Sigrist_, Jan 08 2022