|
Search: id:A164032
|
|
|
| A164032 |
|
Number of "ON" cells in a certain 2-dimensional cellular automaton. |
|
+0
1
|
|
| 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; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
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.
|
|
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.
|
|
CROSSREFS
|
Cf. A048883, A079315, A122108, A160239
Sequence in context: A014717 A104728 A058093 this_sequence A122846 A038294 A145436
Adjacent sequences: A164029 A164030 A164031 this_sequence A164033 A164034 A164035
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
John W. Layman (layman(AT)math.vt.edu), Aug 08 2009
|
|
|
Search completed in 0.002 seconds
|
