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A164032
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Number of "ON" cells in a certain 2-dimensional cellular automaton.
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0
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1, 9, 4, 36, 4, 36, 16, 144, 4, 36, 16, 144, 16, 144, 64, 576, 4, 36, 16, 144, 16, 144, 64, 576, 16, 144, 64, 576, 64, 576, 256, 2304, 4, 36, 16, 144, 16, 144, 64, 576, 16, 144, 64, 576, 64, 576, 256, 2304, 16, 144, 64, 576, 64, 576, 256, 2304, 64, 576, 256, 2304, 256
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| This automaton starts with one ON cell and evolves according to the rule that a cell is ON in a given generation if and only if the number of ON cells, among the cell itself and its eight nearest neighbors, was exactly one in the preceding generation.
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FORMULA
| It appears that this is the self-generating sequence defined by the following process: start with s={1,9} and repeatedly extend by concatenating s with 4*s, thus obtaining {1,9} -> {1,9,4,36} -> {1,9,4,36,4,36,16,144},... , etc.
Also, it appears that if n=2^k+j, with n>2 and 1<=j<=2^k, then a(n)=4a(j), with a(1)=1, a(2)=9.
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CROSSREFS
| Cf. A048883, A079315, A122108, A160239
Sequence in context: A014717 A104728 A058093 * A122846 A038294 A195360
Adjacent sequences: A164029 A164030 A164031 * A164033 A164034 A164035
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KEYWORD
| nonn
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AUTHOR
| John W. Layman (layman(AT)math.vt.edu), Aug 08 2009
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