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A273252 Partial sums of the 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
1, 6, 23, 60, 125, 226, 363, 544, 785, 1094, 1471, 1924, 2461, 3090, 3795, 4584, 5497, 6542, 7719, 9036, 10501, 12122, 13883, 15792, 17881, 20158, 22607, 25236, 28053, 31066, 34211, 37496, 41033, 44830, 48887, 53212, 57813, 62698, 67851, 73280, 79017, 85070 (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=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[Total[Part[on, Range[1, i]]], {i, 1, Length[on]}] (* Sum at each stage *)

CROSSREFS

Cf. A273250.

Sequence in context: A273540 A273214 A273276 * A208598 A119712 A273314

Adjacent sequences:  A273249 A273250 A273251 * A273253 A273254 A273255

KEYWORD

nonn,easy

AUTHOR

Robert Price, May 18 2016

STATUS

approved

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Last modified December 15 01:00 EST 2017. Contains 296020 sequences.