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A271124 First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 286", based on the 5-celled von Neumann neighborhood. 1
4, 7, 5, 20, -9, 48, -31, 67, -40, 81, -32, 83, -59, 156, -105, 148, -67, 127, -44, 137, -125, 260, -143, 251, -204, 313, -168, 327, -336, 469, -248, 355, -308, 533, -372, 491, -412, 561, -336, 519, -456, 653, -484, 719, -628, 785, -500, 735, -676, 921, -660 (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=286; 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. A271121.

Sequence in context: A331138 A051544 A271304 * A336080 A173450 A200386

Adjacent sequences:  A271121 A271122 A271123 * A271125 A271126 A271127

KEYWORD

sign,easy

AUTHOR

Robert Price, Mar 31 2016

STATUS

approved

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Last modified June 24 05:46 EDT 2021. Contains 345416 sequences. (Running on oeis4.)