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A270692 First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 195", based on the 5-celled von Neumann neighborhood. 1
4, 0, 28, -20, 80, -68, 136, -108, 232, -220, 352, -324, 496, -480, 620, -568, 868, -912, 1188, -1236, 1612, -1520, 1672, -1528, 1848, -1836, 2136, -2060, 2492, -2496, 2748, -2624, 3184, -3296, 3928, -3972, 4460, -4280, 4716, -4672, 5252, -5136, 5680, -5684 (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=195; 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. A270689.

Sequence in context: A270281 A270728 A270224 * A282918 A282979 A284086

Adjacent sequences:  A270689 A270690 A270691 * A270693 A270694 A270695

KEYWORD

sign,easy

AUTHOR

Robert Price, Mar 21 2016

STATUS

approved

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Last modified February 23 17:41 EST 2018. Contains 299584 sequences. (Running on oeis4.)