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A173460 Number of "ON" cells at n-th stage in simple 2-dimensional 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 (list; graph; refs; listen; history; text; internal format)
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 n-1. 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 n-1.

- Everything that is already ON remains ON.

A173461, the first differences, gives the number of cells turned "ON" at n-th 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), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-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(n-1) + 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

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Last modified May 31 19:40 EDT 2020. Contains 334748 sequences. (Running on oeis4.)