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 1-5 of 5 results.

A194445 Number of toothpicks or D-toothpicks added at n-th stage to the structure of A194444.

Original entry on oeis.org

0, 1, 2, 4, 4, 4, 8, 11, 8, 4, 8, 16, 24, 12, 20, 25, 16, 4, 8, 16, 24, 28, 36, 42, 44, 20, 24, 40, 64, 32, 44, 53, 32, 4, 8, 16, 24, 28, 36, 44, 52, 42, 48, 60, 100, 68, 84, 83, 84, 28, 24, 44, 72, 84, 104, 116, 132, 54, 56, 92, 144, 72, 92, 109, 64, 4
Offset: 0

Views

Author

Omar E. Pol, Aug 24 2011

Keywords

Comments

Essentially the first differences of A194444.
First differs from A220525 at a(13). - Omar E. Pol, Mar 23 2013

Examples

			Contribution from _Omar E. Pol_, Dec 05 2012 (Start):
Triangle begins:
0;
1;
2;
4,4;
4,8,11,8;
4,8,16,24,12,20,25,16;
4,8,16,24,28,36,42,44,20,24,40,64,32,44,53,32;
(End)

Links

Crossrefs

Row lengths give 1 together with A011782. Right border gives 0 together with A000079.
Cf. A139250, A139251, A172311, A182635, A182839, A194271, A194433, A194435, A194441, A194443, A194444, A212009.

Formula

It appears that a(2^k+1) = 4, if k >= 1.
a(n) = A194435(n)/4. - Omar E. Pol, Mar 23 2013

Extensions

More terms from Omar E. Pol, Mar 23 2013

A194432 D-toothpick sequence starting with a cross formed by 4 toothpicks.

Original entry on oeis.org

0, 4, 12, 28, 44, 60, 88, 136, 168, 184, 216
Offset: 0

Views

Author

Omar E. Pol, Sep 03 2011

Keywords

Comments

On the infinite square grid we start with no toothpicks.
At stage 1, we place a cross, centered at the origin, formed by 2 vertical toothpicks and 2 horizontal toothpicks of length 1. At stage 2, we place 8 D-toothpicks of length sqrt(2). At stage 3, we place 16 toothpicks of length 1. And so on.
The sequence gives the number of toothpicks and D-toothpicks in the structure after n-th stage. The first differences (A194433) give the number of toothpicks and D-toothpicks added at n-th stage.
Apparently this cellular automaton has a fractal (or fractal-like) behavior related to power of 2, similar to A194270 and very similar to A194434. The octagonal structure contains a large number of distinct polygonal shapes. For more information see A194270, A194440 and A194442.

Links

Crossrefs

Cf. A139250, A194270, A194433, A194434, A194440, A194442.

A194435 Number of toothpicks or D-toothpicks added at n-th stage to the structure of A194434.

Original entry on oeis.org

0, 4, 8, 16, 16, 16, 32, 44, 32, 16, 32, 64, 96, 48, 80, 100, 64, 16, 32, 64, 96, 112, 144, 168, 176, 80, 96, 160, 256, 128, 176, 212, 128, 16, 32, 64, 96, 112, 144, 176, 208, 168, 192, 240, 400, 272, 336, 332, 336, 112, 96, 176, 288, 336, 416, 464
Offset: 0

Views

Author

Omar E. Pol, Sep 03 2011

Keywords

Comments

Essentially the first differences of A194434.
First differs from A221528 at a(13). - Omar E. Pol, Mar 23 2013
From Omar E. Pol, Jun 24 2022: (Start)
The word of this cellular automaton is "ab".
For the nonzero terms the structure of the irregular triangle is as shown below:
a,b;
a,b;
a,b,a,b;
a,b,a,b,a,b,a,b;
a,b,a,b,a,b,a,b,a,b,a,b,a,b,a,b;
...
Row lengths are the terms of A011782 multiplied by 2, also the column 2 of A296612.
Columns "a" contain numbers of D-toothpicks (of length sqrt(2)).
Columns "b" contain numbers of toothpicks (of length 1).
An associated sound to the animation could be (tick, tock), (tick, tock), ..., the same as the ticking clock sound.
For further information about the word of cellular automata see A296612. (End)

Examples

			From _Omar E. Pol_, Mar 23 2013: (Start)
When written as an irregular triangle the sequence of nonzeros terms begins:
   4, 8;
  16,16;
  16,32,44,32;
  16,32,64,96, 48, 80,100, 64;
  16,32,64,96,112,144,168,176, 80, 96,160,256,128,176,212,128;
  16,32,64,96,112,144,176,208,168,192,240,400,272,336,332,336,112,96, ...
  ... (End)
Right border gives the powers of 2 >= 8 (reformatted the triangle). - _Omar E. Pol_, Jun 24 2022

Links

Crossrefs

Cf. A011782, A139251, A194271, A194433, A194434, A194441, A194443, A194445, A212009, A221528, A299612.

Formula

a(n) = 4*A194445(n).
Conjecture: a(2^k+1) = 16, if k >= 1.

Extensions

More terms from Omar E. Pol, Mar 23 2013

A212009 Number of toothpicks or D-toothpicks added at n-th stage in the toothpick structure of A212008.

Original entry on oeis.org

0, 1, 4, 8, 16, 22, 20, 24, 36, 40, 32, 44, 56, 94, 60, 56, 76, 72, 32, 48, 72, 112, 132, 140, 136, 168, 112, 132, 140, 238, 148, 120, 156, 136, 32, 48, 72, 112, 132
Offset: 0

Views

Author

Omar E. Pol, Dec 15 2012

Keywords

Comments

Essentially the first differences of A212008.

Examples

			When written as an irregular triangle:
0;
1;
4;
8;
16,22;
20,24,36,40;
32,44,56,94,60,56,76,72;
32,48,72,112,132,140,136,168,112,132,140,238,148,120,156,136;
32,48,72,112,132,...

Links

Crossrefs

Cf. A139250, A139251, A194271, A194433, A194435, A194441, A194443, A194445, A220501.

Formula

It appears that a(2^k + 2) = 32, if k >= 3.

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

Original entry on oeis.org

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

Views

Author

Omar E. Pol, May 13 2013

Keywords

Comments

The first differences of A220512.
First differs from A194433 at a(14).

Examples

			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...

Links

Crossrefs

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.
Showing 1-5 of 5 results.

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