

A273276


Partial sums of the number of active (ON,black) cells in nth stage of growth of twodimensional cellular automaton defined by "Rule 627", based on the 5celled von Neumann neighborhood.


1



1, 6, 23, 60, 121, 222, 343, 516, 733, 1058, 1395, 1836, 2333, 2942, 3599, 4384, 5193, 6234, 7355, 8600, 9957, 11542, 13183, 14936, 16773, 18862, 21155, 23572, 26189, 29006, 31971, 35108, 38405, 42046, 45979, 50160, 54601, 59322, 64147, 69360, 74633, 80246
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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 5Neighbor 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=627; 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+1n, k1+n]], {j, k+1n, k1+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. A273274.
Sequence in context: A009017 A273540 A273214 * A273252 A208598 A119712
Adjacent sequences: A273273 A273274 A273275 * A273277 A273278 A273279


KEYWORD

nonn,easy


AUTHOR

Robert Price, May 18 2016


STATUS

approved



