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.

A194434 D-toothpick sequence of the second kind starting with a X-shaped cross formed by 4 D-toothpicks.

Original entry on oeis.org

0, 4, 12, 28, 44, 60, 92, 136, 168, 184, 216, 280, 376, 424, 504, 604, 668, 684, 716, 780, 876, 988, 1132, 1300, 1476, 1556, 1652, 1812, 2068, 2196, 2372, 2584, 2712, 2728, 2760, 2824, 2920, 3032, 3176, 3352, 3560, 3728, 3920, 4160, 4560, 4832, 5168
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 as a "X", formed by 4 D-toothpicks of length sqrt(2) and centered at the origin. At stage 2, we place 8 toothpicks of length 1. At stage 3, we place 16 D-toothpicks of length sqrt(2). And so on.
The sequence gives the number of toothpicks and D-toothpicks in the structure after n-th stage. The first differences (A194435) give the number of toothpicks or D-toothpicks added at n-th stage.
Apparently this cellular automaton has a fractal behavior (or fractal-like behavior) related to power of 2, similar to A194270 and very similar to A194432. The octagonal structure contains a large number of distinct closed polygonal regions. For more information see A194270, A194440 and A194442.
First differs from A220514 at a(13). - Omar E. Pol, Mar 23 2013
Observation: at least for the terms in the Data section the graph also appears to be a companion of the graph of A187210 but that could be different comparing more terms. - Omar E. Pol, Jun 24 2022

Links

Crossrefs

Cf. A139250, A187210, A194270, A194432, A194435, A194440, A194442, A194444, A212008, A220514.

Formula

a(n) = 4*A194444(n).

Extensions

More terms from Omar E. Pol, Mar 23 2013

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

A194433 Number of toothpicks and D-toothpicks added at n-th stage to the structure of A194432.

Original entry on oeis.org

0, 4, 8, 16, 16, 16, 28, 48, 32, 16, 32
Offset: 0

Views

Author

Omar E. Pol, Sep 03 2011

Keywords

Comments

Essentially the first differences of A194432.

Links

Crossrefs

Cf. A139251, A194271, A194432, A194435, A194441, A194443.

Formula

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

A221528 Number of toothpicks or D-toothpicks added at n-th stage to the structure of A220514.

Original entry on oeis.org

0, 4, 8, 16, 16, 16, 32, 44, 32, 16, 32, 64, 96, 64, 80, 100, 64, 16, 32, 64, 96, 128, 144, 168, 176, 80, 96, 176, 256, 160, 176, 212, 128, 16, 32, 64, 96, 128, 144, 176, 208, 168, 192, 256, 400, 320, 336, 364, 336, 112, 96, 192, 288, 368, 416, 496
Offset: 0

Views

Author

Omar E. Pol, Mar 23 2013

Keywords

Comments

Essentially the first differences of A220514.
First differs from A194435 at a(13).

Examples

			When written as an irregular triangle begins:
0;
4;
8;
16,16;
16,32,44,32;
16,32,64,96,64,80,100,64;
16,32,64,96,128,144,168,176,80,96,176,256,160,176,212,128;
16,32,64,96,128,144,176,208,168,192,256,400,320,336,364,336,112,96,192,288,368,416,496,528,216,224,400,576,352,368, 436,256;

Links

Crossrefs

Row lengths give 1 together with A011782.
Cf. A139251, A194435, A194701, A220501, A220521, A220523, A220525.

Formula

a(n) = 4*A220525(n).

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.
Showing 1-5 of 5 results.

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