

A269696


Number of active (ON,black) cells at stage 2^n1 of the twodimensional cellular automaton defined by "Rule 6", based on the 5celled von Neumann neighborhood.


1



1, 5, 20, 80, 320, 1280, 5120, 20480, 81920, 327680, 1310720, 5242880, 20971520, 83886080, 335544320, 1342177280
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OFFSET

0,2


COMMENTS

Initialized with a single black (ON) cell at stage zero.
Rules 38, 70, 102, 134, 166, 198 and 230 also generate this sequence.
Apparently a duplicate of A003947.  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) = 5*4^(n1) for n>0.
a(n) = 4*a(n1) for n>1.
G.f.: (1+x) / (14*x).
(End)


MATHEMATICA

rule=6; 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. A269695.
Sequence in context: A166859 A167106 A167650 * A167896 A168682 A168730
Adjacent sequences: A269693 A269694 A269695 * A269697 A269698 A269699


KEYWORD

nonn,easy


AUTHOR

Robert Price, Mar 03 2016


EXTENSIONS

a(9)a(15) from Lars Blomberg, Apr 12 2016


STATUS

approved



