A220525 -id:A220525 - cp's OEIS frontend

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

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

Omar E. Pol, Aug 24 2011

Essentially the first differences of A194444.

First differs from A220525 at a(13). - Omar E. Pol, Mar 23 2013

			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)

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.

It appears that a(2^k+1) = 4, if k >= 1.

a(n) = A194435(n)/4. - Omar E. Pol, Mar 23 2013

More terms from Omar E. Pol, Mar 23 2013

A220524 D-toothpick sequence of the third kind in the first quadrant.

Original entry on oeis.org

0, 1, 3, 7, 11, 15, 23, 34, 42, 46, 54, 70, 94, 110, 130, 155, 171, 175, 183, 199, 223, 255, 291, 333, 377, 397, 421, 465, 529, 569, 613, 666, 698, 702, 710, 726, 750, 782, 818, 862, 914, 956, 1004, 1068, 1168, 1248, 1332, 1423, 1507, 1535, 1559, 1607

Offset: 0

Omar E. Pol, Dec 15 2012

nonn

This is a toothpick sequence of forking paths to 135 degrees in the first quadrant. The sequence gives the number of toothpicks and D-toothpicks in the structure after n-th stage. A220525 (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 A194444 at a(13).

Cf. A139250, A194270, A194700, A194444, A220500, A220514, A220520, A220525.

a(n) = A220514(n)/4. - Omar E. Pol, Mar 23 2013

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

Omar E. Pol, Mar 23 2013

Essentially the first differences of A220514.

First differs from A194435 at a(13).

			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;

Row lengths give 1 together with A011782.

Cf. A139251, A194435, A194701, A220501, A220521, A220523, A220525.

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

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

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.

cp's OEIS Frontend

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

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A220524 D-toothpick sequence of the third kind in the first quadrant.

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

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

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