

A173460


Number of "ON" cells at nth stage in simple 2dimensional cellular automaton (see Comments for precise definition).


5



0, 1, 9, 21, 29, 81, 93, 105, 189, 225, 253, 441, 453, 465, 549, 585, 621, 873, 909, 945, 1197, 1305, 1397, 2025, 2037, 2049, 2133, 2169, 2205, 2457, 2493, 2529, 2781, 2889, 2997, 3753, 3789, 3825, 4077, 4185, 4293, 5049, 5157, 5265, 6021, 6345, 6637, 8649
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OFFSET

0,3


COMMENTS

On the infinite square grid, we start at stage 0 with all cells in OFF state. At stage 1, we turn ON a single cell, in the central position.
In order to construct this sequence we use the following rules:
 If n is congruent to 0 (mod 3), we turn "ON" the cells around the vertex of every convex corner formed in the structure at the generation n1. Note that every vertex is surrounded by three new "ON" cells.
 If n is congruent to 1 (mod 3), we turn "ON" the possible bridge cells and the possible peninsula cells (For the definition of bridge cell and of peninsula cell see A160117).
 If n is congruent to 2 (mod 3), we turn "ON" the cells around the cells turned "ON" at the generation n1.
 Everything that is already ON remains ON.
A173461, the first differences, gives the number of cells turned "ON" at nth stage.


LINKS

Lars Blomberg, Table of n, a(n) for n = 0..6000
David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n1)1) for n >= 2.]
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS


FORMULA

a(0)=0, a(n) = a(n1) + A173461(n), n>=1.  [Lars Blomberg, Apr 23 2013]


EXAMPLE

Array begins:
0, 1, 9;
21, 29, 81;
93, 105, 189;
225, 253, 441;
453, 465, 549;
...
If we label the generations of cells turned ON by consecutive numbers we get the cell pattern shown below:
7..7.....7..7
.66.......66.
.65555555556.
7.545545545.7
..553353355..
..553222355..
..545212545..
..553222355..
..553353355..
7.545545545.7
.65555555556.
.66.......66.
7..7.....7..7


CROSSREFS

Cf. A160117, A160118, A173456, A173461, A173462, A173463.
Sequence in context: A039289 A045252 A139538 * A110701 A243703 A133929
Adjacent sequences: A173457 A173458 A173459 * A173461 A173462 A173463


KEYWORD

nonn


AUTHOR

Omar E. Pol, Feb 18 2010


EXTENSIONS

a(18)a(47) from Lars Blomberg, Apr 23 2013


STATUS

approved



