A220527 -id:A220527 - cp's OEIS frontend

A220501 Number of toothpicks or D-toothpicks added at n-th stage in the structure of A220500.

0, 1, 4, 8, 16, 22, 24, 24, 36, 40, 32, 44, 64, 94, 72, 56, 76, 72, 32, 48, 80, 112, 140, 140, 140, 168, 120, 132, 168, 238, 168, 120, 156, 136, 32, 48, 80, 112, 140, 144, 164, 224, 216, 256, 272, 368, 324, 316, 280, 296, 160, 150, 232, 320, 404, 432, 408, 462, 300, 308, 376, 526, 360, 248, 316, 264, 32

Offset: 0

Omar E. Pol, Dec 15 2012

Essentially the first differences of A220500.

			Written as an irregular triangle the sequence begins:
0;
1;
4;
8;
16,22;
24,24,36,40;
32,44,64,94,72,56,76,72;
32,48,80,112,140...
.
From _Omar E. Pol_, May 02 2018: (Start)
Also the nonzero terms can be written as an irregular triangle in which the row lengths are the terms of A011782 multiplied by 2 as shown below:
1,    4;
8,   16;
22,  24, 24, 36;
40,  32, 44, 64,  94,  72,  56,  76;
72,  32, 48, 80, 112, 140, 140, 140, 168, 120, 132, 168, 238, 168, 120, 156;
136, 32, 48, 80, 112, 140, 144, 164, 224, 216, 256, 272, 368, 324, 316, 280, ...
(End)

David Applegate, The movie version
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
Index entries for sequences related to toothpick sequences

Cf. A047999, A139250, A139251, A194271, A194441, A194443, A194701, A220500, A220521, A220523, A220527.

Terms a(23) and beyond from David Applegate's movie version. - Omar E. Pol, May 02 2018

A220525 Number of toothpicks or D-toothpicks added at n-th stage to the structure of A220524.

Original entry on oeis.org

0, 1, 2, 4, 4, 4, 8, 11, 8, 4, 8, 16, 24, 16, 20, 25, 16, 4, 8, 16, 24, 32, 36, 42, 44, 20, 24, 44, 64, 40, 44, 53, 32, 4, 8, 16, 24, 32, 36, 44, 52, 42, 48, 64, 100, 80, 84, 91, 84, 28, 24, 48, 72, 92, 104, 124, 132, 54, 56, 100, 144, 88, 92, 109, 64, 4

Offset: 0

Omar E. Pol, Mar 23 2013

Essentially the first differences of A220524.

First differs from A194445 at a(13).

			When written as an irregular triangle begins:
0;
1;
2;
4,4;
4,8,11,8;
4,8,16,24,16,20,25,16;
4,8,16,24,32,36,42,44,20,24,44,64,40,44,53,32;
4,8,16,24,32,36,44,52,42,48,64,100,80,84,91,84,28,24,48,72,92,104,124,132,54,56,100,144,88,92,109,64;

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

Cf. A139251, A194701, A194445, A220501, A220521, A220524, A220527.

a(n) = A221528(n)/4.

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.

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

A220501 Number of toothpicks or D-toothpicks added at n-th stage in the structure of A220500.

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A220525 Number of toothpicks or D-toothpicks added at n-th stage to the structure of A220524.

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

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