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A269698 First differences of the numbers of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 6", based on the 5-celled von Neumann neighborhood. 1
4, -1, 16, -16, 16, -4, 64, -76, 16, -4, 64, -64, 64, -16, 256, -316, 16, -4, 64, -64, 64, -16, 256, -304, 64, -16, 256, -256, 256, -64, 1024, -1276, 16, -4, 64, -64, 64, -16, 256, -304, 64, -16, 256, -256, 256, -64, 1024, -1264, 64, -16, 256, -256, 256, -64 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Initialized with a single black (ON) cell at stage zero.

Rules 38, 70, 102, 134, 166, 198 and 230 also generate this sequence.

REFERENCES

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

LINKS

Robert Price, Table of n, a(n) for n = 0..299

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 5-Neighbor Cellular Automata

Index to Elementary Cellular Automata

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 *)

Table[on[[i+1]]-on[[i]], {i, 1, Length[on]-1}] (* Difference at each stage *)

CROSSREFS

Cf. A269695.

Sequence in context: A117438 A075499 A099394 * A059991 A002568 A111661

Adjacent sequences:  A269695 A269696 A269697 * A269699 A269700 A269701

KEYWORD

sign,easy

AUTHOR

Robert Price, Mar 03 2016

STATUS

approved

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Last modified October 15 15:14 EDT 2019. Contains 328030 sequences. (Running on oeis4.)