

A269709


Partial sums of the number of active (ON,black) cells in nth stage of growth of twodimensional cellular automaton defined by "Rule 14", based on the 5celled von Neumann neighborhood.


1



1, 6, 14, 34, 54, 86, 126, 202, 270, 350, 438, 562, 686, 846, 1030, 1322, 1582, 1854, 2134, 2450, 2766, 3118, 3494, 3978, 4438, 4934, 5454, 6082, 6710, 7446, 8254, 9386, 10414, 11454, 12502, 13586, 14670, 15790, 16934, 18186, 19414, 20678, 21966, 23362
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OFFSET

0,2


COMMENTS

Initialized with a single black (ON) cell at stage zero.
Rules 46, 142 and 174 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..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 5Neighbor Cellular Automata
Index to Elementary Cellular Automata


MATHEMATICA

rule=14; 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. A269707.
Sequence in context: A279730 A269717 A271097 * A270093 A270735 A270170
Adjacent sequences: A269706 A269707 A269708 * A269710 A269711 A269712


KEYWORD

nonn,easy


AUTHOR

Robert Price, Mar 04 2016


STATUS

approved



