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A269709 Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 14", based on the 5-celled 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 (list; graph; refs; listen; history; text; internal format)
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 5-Neighbor 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

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Last modified March 5 16:55 EST 2021. Contains 341827 sequences. (Running on oeis4.)