

A272091


Partial sums of the number of active (ON,black) cells in nth stage of growth of twodimensional cellular automaton defined by "Rule 425", based on the 5celled von Neumann neighborhood.


1



1, 5, 14, 42, 59, 127, 168, 308, 341, 601, 706, 1054, 1135, 1619, 1788, 2408, 2473, 3501, 3702, 4882, 5091, 6311, 6672, 8092, 8253, 10369, 10858, 13062, 13399, 15867, 16548, 19152, 19281, 23381, 23774, 28154, 28555, 32975, 33656, 38404, 38821, 44457, 45714
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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=425; 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. A272089.
Sequence in context: A122485 A198086 A272018 * A270722 A272282 A270893
Adjacent sequences: A272088 A272089 A272090 * A272092 A272093 A272094


KEYWORD

nonn,easy


AUTHOR

Robert Price, Apr 19 2016


STATUS

approved



