cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A220527 Number of toothpicks or D-toothpicks added at n-th stage in the toothpick structure of A220526.

Original entry on oeis.org

0, 1, 2, 4, 4, 4, 4, 7, 8, 4, 4, 8, 12, 14, 12, 15, 16, 4, 4, 8, 12, 16, 10, 24, 26
Offset: 0

Views

Author

Omar E. Pol, Jan 02 2013

Keywords

Comments

Essentially the first differences of A220526.

Examples

			Written as an irregular triangle begins:
0;
1;
2;
4,4;
4,4,7,8;
4,4,8,12,14,12,15,16;
4,4,8,12,16,10,24,26,...

Links

Crossrefs

Cf. A139250, A139251, A194271, A194441, A194443, A220501, A220521, A220523, A220526.

A220512 D-toothpick sequence of the third kind starting with a cross formed by 4 toothpicks.

Original entry on oeis.org

0, 4, 12, 28, 44, 60, 88, 136, 168, 184, 216, 280, 344, 424, 508, 620, 684, 700, 732, 796, 892, 1004, 1148, 1324, 1460, 1572, 1668, 1844, 2020, 2228, 2424, 2664, 2792, 2808, 2840, 2904, 3000, 3112, 3264
Offset: 0

Views

Author

Omar E. Pol, Dec 15 2012

Keywords

Comments

This is a toothpick sequence of forking paths to 135 degrees. The sequence gives the number of toothpicks and D-toothpicks in the structure after n-th stage. A221565 (the first differences) give the number of toothpicks or D-toothpicks added at n-th stage. It appears that the structure has a fractal (or fractal-like) behavior. For more information see A194700.
First differs from A194432 at a(14).

Links

Crossrefs

Cf. A139250, A194270, A194432, A194700, A220500, A220514, A220520, A220522, A220524, A220526.

A230978 a(n) = (A220500(n) - 1)/2.

Original entry on oeis.org

0, 2, 6, 14, 25, 37, 49, 67, 87, 103, 125, 157, 204, 240, 268, 306, 342, 358, 382, 422, 478, 548, 618, 688, 772, 832, 898, 982, 1101, 1185, 1245, 1323, 1391, 1407, 1431, 1471, 1527, 1597, 1669, 1751, 1863, 1971, 2099, 2235, 2419, 2581, 2739, 2879, 3027, 3107, 3182, 3298, 3458, 3660, 3876, 4080
Offset: 1

Views

Author

Omar E. Pol, Nov 30 2013

Keywords

Links

Crossrefs

Cf. A139250, A220500, A220520, A220522, A220526.

Extensions

More terms added using the data at A220500 by Amiram Eldar, May 06 2024

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

Views

Author

Omar E. Pol, Dec 07 2013

Keywords

Comments

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?

Links

Crossrefs

Cf. A139250, A194276, A220500, A220512, A220514, A220520, A220522, A220524, A220526.
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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