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A261692 Number of "ON" cells after n-th stage in a cellular automaton in a 90-degree wedge on the square grid. (See Comments lines for definition.) 4
0, 1, 4, 5, 12, 17, 20, 21, 36, 49, 60, 69, 76, 81, 84, 85, 116, 145, 172, 197, 220, 241, 260, 277, 292, 305, 316, 325, 332, 337, 340, 341, 404, 465, 524, 581, 636, 689, 740, 789, 836, 881, 924, 965, 1004, 1041, 1076, 1109, 1140, 1169, 1196, 1221, 1244, 1265, 1284, 1301, 1316, 1329, 1340, 1349, 1356, 1361, 1364, 1365, 1492 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
In order to construct the structure we use the following rules:
- On the square grid we are in a 90-degree wedge with the vertex located on top of the wedge.
- At stage 0 there are no ON cells, so a(0) = 0.
- At stage 1 we turn ON the nearest cell of the vertex, so a(1) = 1.
- The cells turned ON remain ON forever.
- If n is a power of 2, at stage n we turn "ON" 2*n - 1 connected cells in the n-th row of the structure.
- Otherwise, if n is not a power of 2, at stage n we turn "ON" k - 2 connected cells in the n-th row of the structure, where k is the number of ON cells in row n - 1.
- The "ON" cells of row n must be centered respect to the "ON" cells of row n - 1.
Note that the structure seems to grow into the holes of a virtual structure similar to the Sierpiński's triangle but using square cells (see example).
A261693 gives the number of cells turned "ON" at n-th stage.
This is analog of A255748, but here we are working on the square grid.
LINKS
FORMULA
a(n) = (A262620(n) - 1)/4.
EXAMPLE
Illustration of initial terms (n = 0..15):
------------------------------------------------------
n A261692(n) a(n) Diagram
------------------------------------------------------
0 0 0 /_\
1 1 1 /_|_|_\
2 3 4 / |_|_|_| \
3 1 5 /_ _ _|_|_ _ _\
4 7 12 / |_|_|_|_|_|_|_| \
5 5 17 / |_|_|_|_|_| \
6 3 20 / |_|_|_| \
7 1 21 /_ _ _ _ _ _ _|_|_ _ _ _ _ _ _\
8 15 36 / |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_| \
9 13 49 |_|_|_|_|_|_|_|_|_|_|_|_|_|
10 11 60 |_|_|_|_|_|_|_|_|_|_|_|
11 9 69 |_|_|_|_|_|_|_|_|_|
12 7 76 |_|_|_|_|_|_|_|
13 5 81 |_|_|_|_|_|
14 3 84 |_|_|_|
15 1 85 |_|
...
After 15 generations there are 85 ON cells in the structure, so a(15) = 85.
CROSSREFS
Sequence in context: A131116 A352215 A342324 * A131328 A054451 A309479
KEYWORD
nonn,look
AUTHOR
Omar E. Pol, Sep 25 2015
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)