A220512 -id:A220512 - cp's OEIS frontend

A221565 Number of toothpicks or D-toothpicks added at n-th stage to the structure of A220512.

0, 4, 8, 16, 16, 16, 28, 48, 32, 16, 32, 64, 64, 80, 84, 112, 64, 16, 32, 64, 96, 112, 144, 176, 136, 112, 96, 176, 176, 208, 196, 240, 128, 16, 32, 64, 96, 112, 152

Offset: 0

Omar E. Pol, May 13 2013

The first differences of A220512.

First differs from A194433 at a(14).

			When written as a irregular triangle begins:
0;
4;
8;
16,16;
16,28,48,32;
16,32,64,64,80,84,112,64;
16,32,64,96,112,144,176,136,112,96,176,176,208,196,240,128;
16,32,64,96,112,152...

Row lengths give 1 together with A011782. Right border gives 0 together with four times A000079.

Cf. A139251, A194271, A194701, A194443, A220501, A220512, A220521, A220523, A220525, A220527, A221528.

A220526 Number of toothpicks and D-toothpicks after n-th stage in the structure of the D-toothpick "medium" triangle of the third kind.

Original entry on oeis.org

0, 1, 3, 7, 11, 15, 19, 26, 34, 38, 42, 50, 62, 76, 88, 103, 119, 123, 127, 135, 147, 163, 183, 207, 233

Offset: 0

Omar E. Pol, Jan 02 2013

The structure is essentially one of the horizontal wedges of A220500. First differs from A194442 (and from A220522) at a(13). A220527 (the first differences) give the number of toothpicks or D-toothpicks added at n-th stage.

Cf. A139250, A194270, A194440, A194700, A194442, A220500, A220512, A220514, A220520, A220522, A220524, A220527.

A231346 Number of distinct polygonal shapes after n-th stage in the structure of the D-toothpick cellular automaton of A220500.

Original entry on oeis.org

0, 0, 0, 1, 3, 4, 5, 7, 8, 8, 8, 11, 15, 17, 18, 19, 19, 19, 19, 19, 22

Offset: 1

Omar E. Pol, Dec 07 2013

The cellular automaton of A220500 contains a large number of distinct polygonal shapes. The exact number is unknown. Apparently it's greater than 63.
For simplicity we also call polygonal shapes "polygons".
In order to construct this sequence we use the following rules:
- Consider only the convex polygons and the concave polygons. Self-intersecting polygons are not counted.
- Unfinished polygons with inward growth are not counted.
- If two polygons have the same shape but they have different size then these polygons must be counted as distinct polygonal shapes.
- The reflected shapes of asymmetric polygons, both with the same area, must be counted as distinct polygonal shapes.
Question: Is there a maximal record in this sequence?

Omar E. Pol, Illustration of the structure of A220500 after 17 stages, (Contains 19 distinct polygonal shapes.)
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
Index entries for sequences related to toothpick sequences

Cf. A139250, A194276, A220500, A220512, A220514, A220520, A220522, A220524, A220526.

cp's OEIS Frontend

A221565 Number of toothpicks or D-toothpicks added at n-th stage to the structure of A220512.

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A220526 Number of toothpicks and D-toothpicks after n-th stage in the structure of the D-toothpick "medium" triangle of the third kind.

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A231346 Number of distinct polygonal shapes after n-th stage in the structure of the D-toothpick cellular automaton of A220500.

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