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A269713
Partial sums of the 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
1, 5, 13, 25, 45, 69, 113, 141, 193, 249, 353, 409, 513, 625, 837, 897, 1013, 1133, 1365, 1485, 1717, 1957, 2421, 2541, 2773, 3013, 3477, 3717, 4181, 4661, 5593, 5717, 5961, 6209, 6697, 6945, 7433, 7929, 8905, 9153, 9641, 10137, 11113, 11609, 12585, 13577
OFFSET
0,2
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[Total[Part[on, Range[1, i]]], {i, 1, Length[on]}] (* Sum at each stage *)
CROSSREFS
Cf. A269711.
Sequence in context: A102724 A147031 A147220 * A196069 A147182 A146175
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 04 2016
STATUS
approved