

A269712


Number of active (ON,black) cells at stage 2^n1 of the twodimensional cellular automaton defined by "Rule 20", based on the 5celled von Neumann neighborhood.


0



1, 4, 12, 28, 60, 124, 252, 508, 1020, 2044, 4092, 8188, 16380, 32764, 65532, 131068
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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.
Apparently a duplicate of A173033.  R. J. Mathar, Mar 09 2016


REFERENCES

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.


LINKS

Table of n, a(n) for n=0..15.
N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015.
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
S. Wolfram, A New Kind of Science
Index entries for sequences related to cellular automata
Index to 2D 5Neighbor Cellular Automata
Index to Elementary Cellular Automata


FORMULA

Conjectures from Colin Barker, Mar 08 2016: (Start)
a(n) = 4*(2^n1) =A028399(n+2) for n>0.
a(n) = 3*a(n1)2*a(n2) for n>2.
G.f.: (1+x+2*x^2) / ((1x)*(12*x)).
(End)


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 *)
Part[on, 2^Range[0, Log[2, stages]]] (* Extract relevant terms *)


CROSSREFS

Cf. A269711.
Sequence in context: A261320 A179023 A321690 * A028399 A173033 A339124
Adjacent sequences: A269709 A269710 A269711 * A269713 A269714 A269715


KEYWORD

nonn,more


AUTHOR

Robert Price, Mar 04 2016


EXTENSIONS

a(9)a(15) from Lars Blomberg, Apr 15 2016


STATUS

approved



