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A273253 First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 619", based on the 5-celled von Neumann neighborhood. 1
4, 12, 20, 28, 36, 36, 44, 60, 68, 68, 76, 84, 92, 76, 84, 124, 132, 132, 140, 148, 156, 140, 148, 180, 188, 172, 180, 188, 196, 132, 140, 252, 260, 260, 268, 276, 284, 268, 276, 308, 316, 300, 308, 316, 324, 260, 268, 372, 380, 364, 372, 380, 388, 324, 332 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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..127

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=619; 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 *)

Table[on[[i+1]]-on[[i]], {i, 1, Length[on]-1}] (* Difference at each stage *)

CROSSREFS

Cf. A273250.

Sequence in context: A213258 A141065 A190748 * A328304 A031065 A017113

Adjacent sequences:  A273250 A273251 A273252 * A273254 A273255 A273256

KEYWORD

nonn,easy

AUTHOR

Robert Price, May 18 2016

STATUS

approved

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Last modified November 18 12:35 EST 2019. Contains 329261 sequences. (Running on oeis4.)