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A271097 Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 278", based on the 5-celled von Neumann neighborhood. 1
1, 6, 14, 34, 50, 94, 126, 214, 258, 390, 450, 646, 735, 992, 1092, 1424, 1589, 2014, 2174, 2686, 2935, 3572, 3804, 4524, 4869, 5794, 6126, 7122, 7587, 8820, 9248, 10524, 11084, 12596, 13152, 14808, 15464, 17328, 18025, 20078, 20882, 23170, 23994, 26446 (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=278; 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. A271095.

Sequence in context: A066510 A279730 A269717 * A269709 A270093 A270735

Adjacent sequences:  A271094 A271095 A271096 * A271098 A271099 A271100

KEYWORD

nonn,easy

AUTHOR

Robert Price, Mar 30 2016

STATUS

approved

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Last modified April 15 10:27 EDT 2021. Contains 342977 sequences. (Running on oeis4.)