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A273273 First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 625", based on the 5-celled von Neumann neighborhood. 1
3, 17, 8, 43, 12, 57, 27, 92, 29, 80, 15, 144, 36, 120, 44, 220, 28, 188, 68, 180, 4, 181, 108, 359, 49, 248, -45, 372, 88, 237, -24, 503, 101, 276, 248, 336, 31, 309, 76, 460, 187, 493, -68, 467, 16, 588, 21, 692, -60, 447, 237, 508, 164, 355, 245, 640, 152 (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=625; 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. A273270.

Sequence in context: A124689 A093844 A273211 * A273249 A273303 A033467

Adjacent sequences:  A273270 A273271 A273272 * A273274 A273275 A273276

KEYWORD

sign,easy

AUTHOR

Robert Price, May 18 2016

STATUS

approved

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Last modified March 5 15:22 EST 2021. Contains 341825 sequences. (Running on oeis4.)