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A269755 Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 30", based on the 5-celled von Neumann neighborhood. 1
1, 6, 18, 34, 70, 94, 154, 198, 314, 358, 486, 606, 806, 950, 1210, 1454, 1750, 2018, 2386, 2778, 3166, 3550, 4042, 4634, 5198, 5702, 6458, 7250, 8006, 8718, 9610, 10670, 11506, 12382, 13534, 14834, 16058, 17150, 18462, 20150, 21546, 22858, 24642, 26618 (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=30; 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. A269753.

Sequence in context: A323148 A181510 A301715 * A270135 A038343 A271123

Adjacent sequences:  A269752 A269753 A269754 * A269756 A269757 A269758

KEYWORD

nonn,easy

AUTHOR

Robert Price, Mar 04 2016

STATUS

approved

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Last modified September 22 17:39 EDT 2021. Contains 347607 sequences. (Running on oeis4.)