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A271162 Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 305", based on the 5-celled von Neumann neighborhood. 1
1, 5, 10, 42, 51, 151, 172, 372, 405, 721, 770, 1218, 1287, 1911, 1992, 2852, 2953, 4013, 4154, 5478, 5663, 7295, 7504, 9448, 9693, 11957, 12226, 14846, 15171, 18175, 18564, 22012, 22473, 26337, 26806, 31226, 31711, 36567, 37152, 42544, 43281, 49345, 50050 (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..128

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

CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];

code=305; stages=128;

rule=IntegerDigits[code, 2, 10];

g=2*stages+1; (* Maximum size of grid *)

a=PadLeft[{{1}}, {g, g}, 0, Floor[{g, g}/2]]; (* Initial ON cell on grid *)

ca=a;

ca=Table[ca=CAStep[rule, ca], {n, 1, stages+1}];

PrependTo[ca, a];

(* Trim full grid to reflect growth by one cell at each stage *)

k=(Length[ca[[1]]]+1)/2;

ca=Table[Table[Part[ca[[n]][[j]], Range[k+1-n, k-1+n]], {j, k+1-n, k-1+n}], {n, 1, k}];

on=Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *)

CROSSREFS

Cf. A271160.

Sequence in context: A269812 A271127 A270016 * A269874 A270077 A271150

Adjacent sequences:  A271159 A271160 A271161 * A271163 A271164 A271165

KEYWORD

nonn,easy

AUTHOR

Robert Price, Mar 31 2016

STATUS

approved

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Last modified May 7 10:18 EDT 2021. Contains 343650 sequences. (Running on oeis4.)