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A269717 Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 22", based on the 5-celled von Neumann neighborhood. 1
1, 6, 14, 34, 50, 94, 126, 214, 246, 338, 402, 586, 650, 834, 962, 1330, 1394, 1582, 1710, 2086, 2214, 2590, 2846, 3598, 3726, 4102, 4358, 5110, 5366, 6118, 6630, 8134, 8262, 8642, 8898, 9658, 9914, 10674, 11186, 12706, 12962, 13722, 14234, 15754, 16266 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

REFERENCES

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

LINKS

Robert Price, Table of n, a(n) for n = 0..300

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=22; 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. A269715.

Sequence in context: A074981 A066510 A279730 * A271097 A269709 A270093

Adjacent sequences:  A269714 A269715 A269716 * A269718 A269719 A269720

KEYWORD

nonn,easy

AUTHOR

Robert Price, Mar 04 2016

STATUS

approved

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Last modified April 16 12:45 EDT 2021. Contains 343037 sequences. (Running on oeis4.)