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A269714
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 20", based on the 5-celled von Neumann neighborhood.
1
3, 4, 4, 8, 4, 20, -16, 24, 4, 48, -48, 48, 8, 100, -152, 56, 4, 112, -112, 112, 8, 224, -344, 112, 8, 224, -224, 224, 16, 452, -808, 120, 4, 240, -240, 240, 8, 480, -728, 240, 8, 480, -480, 480, 16, 960, -1704, 240, 8, 480, -480, 480, 16, 960, -1456, 480
OFFSET
0,1
COMMENTS
Initialized with a single black (ON) cell at stage zero.
Rules 28, 52, 60, 148, 156, 180, 188, 532, 540, 564, 572, 660, 668, 692 and 700 also generate this sequence.
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
MATHEMATICA
rule=20; stages=300;
ca=CellularAutomaton[{rule, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, stages]; (* Start with single black cell *)
on=Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *)
Table[on[[i+1]]-on[[i]], {i, 1, Length[on]-1}] (* Difference at each stage *)
CROSSREFS
Cf. A269711.
Sequence in context: A161496 A010612 A021033 * A146944 A294113 A339827
KEYWORD
sign,easy
AUTHOR
Robert Price, Mar 04 2016
STATUS
approved