A269754 - OEIS

A269754

Number of active (ON, black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by "Rule 30", based on the 5-celled von Neumann neighborhood.

1, 5, 16, 44, 244, 1060, 4368, 15464, 62400, 244004, 975416, 3897600, 15566124, 62168524, 248974720, 996841660

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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

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 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 *)

Part[on, 2^Range[0, Log[2, stages]]] (* Extract relevant terms *)

CROSSREFS

Cf. A269753.

Sequence in context: A048777 A300961 A270134 * A282425 A185003 A189390

Adjacent sequences: A269751 A269752 A269753 * A269755 A269756 A269757

KEYWORD

nonn,more

AUTHOR

Robert Price, Mar 04 2016

EXTENSIONS

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

STATUS

approved