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 1-8 of 8 results.

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

Original entry on oeis.org

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

Views

Author

Omar E. Pol, Dec 15 2012

Keywords

Comments

Essentially the first differences of A220500.

Examples

			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)

Links

Crossrefs

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

Extensions

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

A220522 Number of toothpicks and D-toothpicks after n-th stage in the D-toothpick "narrow" triangle of the third kind.

Original entry on oeis.org

0, 1, 3, 7, 11, 15, 19, 26, 34, 38, 42, 50, 62, 70, 78, 91, 107, 111, 115, 123, 135, 151, 167, 187, 211, 223, 231, 247, 275, 291, 307, 332, 364, 368, 372, 380, 392, 408, 424, 446, 478, 504, 524, 548, 588, 620, 660, 701, 749, 769, 777
Offset: 0

Views

Author

Omar E. Pol, Dec 15 2012

Keywords

Comments

The structure is essentially one of the oblique wedges of several D-toothpick structures. For more information see A220500. First differs from A194442 at a(47). The first differences (A220523) give the number of toothpicks or D-toothpicks added at n-th stage.

Links

Crossrefs

Cf. A047999, A139250, A194270, A194700, A194440, A194442, A194444, A220496, A220500, A220523.

A220521 Number of toothpicks or D-toothpicks added at n-th stage in the toothpick structure of A220520.

Original entry on oeis.org

1, 2, 4, 4, 4, 4, 8, 8, 4, 4, 8, 12, 16, 12, 16, 16, 4, 4, 8, 12, 16, 20, 24, 26, 24, 12, 20, 32, 40, 28, 32, 32, 4, 4, 8, 12, 16, 20, 24, 26, 24, 20, 32, 44, 64, 52, 48, 54, 40, 12, 20, 36, 48, 56, 64, 74, 76, 30, 44, 72, 88, 60, 64, 64, 4, 4, 8, 12
Offset: 1

Views

Author

Omar E. Pol, Dec 15 2012

Keywords

Comments

From Omar E. Pol, Apr 26 2020: (Start)
The cellular automaton described in A220520 has word "ab", so the structure of this triangle is as follows:
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;
...
The row lengths are the terms of A011782 multiplied by 2, equaling the column 2 of the square array A296612: 2, 2, 4, 8, 16, ...
This arrangement has the property that the odd-indexed columns (a) contain numbers of the toothpicks of length 1, and the even-indexed columns (b) contain numbers of the D-toothpicks.
For further information about the "word" of a cellular automaton see A296612. (End)

Examples

			Written as an irregular triangle the sequence begins:
1,2;
4,4;
4,4,8,8;
4,4,8,12,16,12,16,16;
4,4,8,12,16,20,24,26,24,12,20,32,40,28,32,32;
4,4,8,12,16,20,24,26,24,20,32,44,64,52,48,54,40,12,20,...
Triangle reformatted by _Omar E. Pol_, Apr 26 2020

Links

Crossrefs

First differences of A220520.
First differs from A194441 at a(14).
Columns 1-3: A123932, A040002, A010731.
Cf. A139250, A139251, A194443, A220501, A220523, A296612.

Extensions

0 removed and offset changed by Omar E. Pol, Apr 26 2020

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.

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).

A220497 Number of toothpicks or D-toothpicks added at n-th stage to the structure of A220496.

Original entry on oeis.org

0, 1, 2, 4, 4, 4, 4, 7, 8, 4, 4, 8, 8, 8, 8, 13, 16, 4, 4, 8, 8, 8, 8, 14, 16, 8, 8, 16, 16, 16, 16, 25, 32, 4, 4, 8, 8, 8, 8, 14, 16, 8, 8, 16, 16, 16, 16, 26, 32, 8, 8, 16, 16, 16, 16, 28, 32, 16, 16, 32, 32, 32, 32, 49, 64, 4, 4, 8, 8, 8, 8, 14, 16
Offset: 0

Views

Author

Omar E. Pol, Dec 23 2012

Keywords

Comments

Essentially the first differences of A220496.
First differs from A194443 (and from A220523) at a(12).

Examples

			Written as an irregular triangle begins:
0;
1;
2;
4,4;
4,4,7,8;
4,4,8,8,8,8,13,16;
4,4,8,8,8,8,14,16,8,8,16,16,16,16,25,32;
4,4,8,8,8,8,14,16,8,8,16,16,16,16,26,32,8,8,16,16,16,16,28,32,16,16,32,32,32,32,49,64;

Links

Crossrefs

Cf. A139250, A139251, A194271, A194443, A194700, A194701, A220495, A220496, A220523.

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.

A233763 Number of toothpicks or D-toothpicks added at n-th stage in the structure of the D-toothpick "narrow" triangle of A233762.

Original entry on oeis.org

0, 1, 2, 2, 4, 2, 4, 5, 8, 2, 4, 6, 12, 6, 8, 11, 16, 2, 4, 6, 12, 14, 16, 18, 24, 10, 8, 14, 28, 14, 16, 23, 32, 2, 4, 6, 12, 14, 16, 20, 32, 24, 20, 22, 40, 30, 40, 39, 48, 18, 8
Offset: 0

Views

Author

Omar E. Pol, Dec 15 2013

Keywords

Comments

Essentially the first differences of A233762.

Examples

			Written as an irregular triangle in which the row lengths is A011782 the sequence (starting from 1) begins:
1;
2;
2,4;
2,4,5,8;
2,4,6,12,6,8,11,16;
2,4,6,12,14,16,18,24,10,8,14,28,14,16,23,32;
2,4,6,12,14,16,20,32,24,20,22,40,30,40,39,48,18,8,...
Right border gives A000079.

Links

Crossrefs

Cf. A000079, A011782, A139251, A220501, A220523, A233761, A233762.

Formula

a(2n) = A220523(2n); a(2n+1) = A220523(2n+1) - 2.
Showing 1-8 of 8 results.

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