

A269713


Partial sums of the number of active (ON,black) cells in nth stage of growth of twodimensional cellular automaton defined by "Rule 20", based on the 5celled 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
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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.


LINKS



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



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



