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A269567 Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 622", based on the 5-celled von Neumann neighborhood. 1
1, 6, 15, 36, 61, 98, 155, 224, 313, 414, 535, 668, 837, 1042, 1299, 1608, 1969, 2302, 2679, 3060, 3445, 3906, 4371, 4880, 5481, 6134, 6831, 7612, 8501, 9346, 10443, 11520, 12873, 14078, 15383, 16732, 18077, 19434, 20755, 22192, 23745, 25334, 26935, 28644 (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, 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=622; 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]}]

CROSSREFS

Cf. A269522.

Sequence in context: A273390 A273451 A272928 * A253098 A272989 A273644

Adjacent sequences:  A269564 A269565 A269566 * A269568 A269569 A269570

KEYWORD

nonn,easy

AUTHOR

Robert Price, Feb 29 2016

STATUS

approved

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Last modified January 22 00:08 EST 2022. Contains 350481 sequences. (Running on oeis4.)