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A272018 Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 417", based on the 5-celled von Neumann neighborhood. 1
1, 5, 14, 42, 59, 127, 168, 308, 341, 601, 702, 1042, 1103, 1639, 1808, 2428, 2493, 3521, 3718, 4890, 5075, 6355, 6720, 8136, 8301, 10397, 10870, 13014, 13323, 15835, 16472, 19020, 19329, 22873, 23602, 27126, 27675, 31595, 32568, 36508, 37153, 42081, 43262 (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=417; 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[Total[Part[on, Range[1, i]]], {i, 1, Length[on]}] (* Sum at each stage *)

CROSSREFS

Cf. A272016.

Sequence in context: A171185 A122485 A198086 * A272091 A270722 A272282

Adjacent sequences:  A272015 A272016 A272017 * A272019 A272020 A272021

KEYWORD

nonn,easy

AUTHOR

Robert Price, Apr 17 2016

STATUS

approved

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Last modified January 23 03:02 EST 2021. Contains 340384 sequences. (Running on oeis4.)