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 1-10 of 12 results. Next

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

A220520 Number of toothpicks and D-toothpicks after n-th stage in the D-toothpick "wide" triangle of the third kind.

Original entry on oeis.org

0, 1, 3, 7, 11, 15, 19, 27, 35, 39, 43, 51, 63, 79, 91, 107, 123, 127, 131, 139, 151, 167, 187, 211, 237, 261, 273, 293, 325, 365, 393, 425, 457, 461, 465, 473, 485, 501, 521, 545, 571, 595, 615, 647, 691, 755, 807, 855, 909, 944, 961, 981, 1017, 1065
Offset: 0

Views

Author

Omar E. Pol, Dec 15 2012

Keywords

Comments

The structure is essentially one of the vertical wedges of several D-toothpick structures. For more information see A220500. First differs from A194440 at a(14). The first differences (A220521) give the number of toothpicks or D-toothpicks added at n-th stage. See A220522 for the "narrow" triangle of the third kind.

Links

Crossrefs

Cf. A047999, A139250, A194270, A194440, A194442, A220494, A220521, A220522.

A220523 Number of toothpicks or D-toothpicks added at n-th stage in the structure of the D-toothpick "narrow" triangle of A220522.

Original entry on oeis.org

0, 1, 2, 4, 4, 4, 4, 7, 8, 4, 4, 8, 12, 8, 8, 13, 16, 4, 4, 8, 12, 16, 16, 20, 24, 12, 8, 16, 28, 16, 16, 25, 32, 4, 4, 8, 12, 16, 16, 22, 32, 26, 20, 24, 40, 32, 40, 41, 48, 20, 8
Offset: 0

Views

Author

Omar E. Pol, Dec 15 2012

Keywords

Comments

Essentially the first differences of A220522. First differs from A194443 at a(47).

Examples

			Written as an irregular triangle begins:
0;
1;
2;
4,4;
4,4,7,8;
4,4,8,12,8,8,13,16;
4,4,8,12,16,16,20,24,12,8,16,28,16,16,25,32;
4,4,8,12,16,16,22,32,26,20,24,40,32,40,41,48,20,8,...

Links

Crossrefs

Cf. A139250, A139251, A194441, A194443, A194445, A220521, A220522.

A233781 Number of toothpicks or D-toothpicks added at n-th stage to the structure of the D-toothpick "wide" triangle of A233780.

Original entry on oeis.org

0, 1, 2, 2, 4, 2, 4, 6, 8, 2, 4, 6, 10, 10, 8, 14, 16, 2, 4, 6, 10, 10, 10, 18, 24, 18, 8, 14, 22, 26, 16, 30, 32, 2, 4, 6, 10, 10, 10, 18, 24, 18, 10, 18, 30, 38, 26, 42, 52, 34, 8, 14, 22, 26, 22, 42, 56, 50, 16, 30, 46, 58, 32, 62, 64, 2, 4, 6, 10, 10
Offset: 0

Views

Author

Omar E. Pol, Dec 15 2013

Keywords

Comments

Essentially the first differences of A233780.
First differs from A170905 at a(24).
First differs from A233971 at a(25).
First differs from A233765 at a(44).

Examples

			Written as an irregular triangle in which the row lengths is A011782 the sequence (starting from 1) begins:
1;
2;
2,4;
2,4,6,8;
2,4,6,10,10,8,14,16;
2,4,6,10,10,10,18,24,18,8,14,22,26,16,30,32;
2,4,6,10,10,10,18,24,18,10,18,30,38,26,42,52,34,8,14,22,26,22,42,56,50,16,30,46,58,32,62,64;
Right border gives A000079.

Links

Crossrefs

Cf. A000079, A011782, A139251, A170905, A220501, A220521, A231349, A233765, A233780, A233782, A233971.

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

Views

Author

Omar E. Pol, Mar 23 2013

Keywords

Comments

Essentially the first differences of A220524.
First differs from A194445 at a(13).

Examples

			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;

Links

Crossrefs

Row lengths give 1 together with A011782. Right border gives 0 together with A000079.
Cf. A139251, A194701, A194445, A220501, A220521, A220524, A220527.

Formula

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

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).

A233761 Number of toothpicks or D-toothpicks added at n-th stage in the structure of the D-toothpick "wide" triangle of A233760.

Original entry on oeis.org

0, 1, 2, 2, 4, 2, 4, 6, 8, 2, 4, 6, 12, 14, 12, 14, 16, 2, 4, 6, 12, 14, 20, 22, 26, 22, 12, 18, 32, 38, 28, 30, 32, 2, 4, 6, 12, 14, 20, 22, 26, 22, 20, 30, 44, 62, 52, 46, 54, 38, 12, 18, 36, 46, 56, 62, 74, 74, 30, 42, 72, 86, 60, 62, 64, 2, 4, 6, 12
Offset: 0

Views

Author

Omar E. Pol, Dec 16 2013

Keywords

Comments

Essentially the first differences of A233760.

Examples

			Written as an irregular triangle in which the row lengths is A011782 the sequence (starting from 1) begins:
1;
2;
2,4;
2,4,6,8;
2,4,6,12,14,12,14,16;
2,4,6,12,14,20,22,26,22,12,18,32,38,28,30,32;
2,4,6,12,14,20,22,26,22,20,30,44,62,52,46,54,38,12,18,36,46,56,62,74,74,30,42,72,86,60,62,64;
Right border gives A000079.

Links

Crossrefs

Cf. A000079, A011782, A139251, A220501, A220521, A233760, A233763, A233781.

Formula

a(2n) = A220521(2n); a(2n+1) = A220521(2n+1) - 2.

A233765 Number of toothpicks or D-toothpicks added at n-th stage to the structure of the toothpick "wide" triangle of A233764.

Original entry on oeis.org

0, 1, 2, 2, 4, 2, 4, 6, 8, 2, 4, 6, 10, 10, 8, 14, 16, 2, 4, 6, 10, 10, 10, 18, 24, 18, 8, 14, 22, 26, 16, 30, 32, 2, 4, 6, 10, 10, 10, 18, 24, 18, 10, 18, 28, 38, 30, 50, 54, 34, 8, 14, 22, 26, 22, 42, 56, 50, 16, 30, 46, 58, 32, 62, 64, 2, 4, 6, 10, 10
Offset: 0

Views

Author

Omar E. Pol, Dec 16 2013

Keywords

Comments

Essentially the first differences of A233764.
First differs from A170905 at a(24).
First differs from A233971 at a(25).
First differs from A233781 at a(44).

Examples

			Written as an irregular triangle in which the row lengths is A011782 the sequence (starting from 1) begins:
1;
2;
2,4;
2,4,6,8;
2,4,6,10,10,8,14,16;
2,4,6,10,10,10,18,24,18,8,14,22,26,16,30,32;
2,4,6,10,10,10,18,24,18,10,18,28,38,30,50,54,34,8,14,22,26,22,42,56,50,16,30,46,58,32,62,64;
Right border gives A000079.

Links

Crossrefs

Cf. A000079, A011782, A139251, A220501, A220521, A231349, A233764, A233781, A233971.

A220495 Number of toothpicks or D-toothpicks added at n-th stage to the structure of A220494.

Original entry on oeis.org

0, 1, 2, 4, 4, 4, 4, 8, 8, 4, 4, 8, 8, 8, 8, 16, 16, 4, 4, 8, 8, 8, 8, 16, 16, 8, 8, 16, 16, 16, 16, 32, 32, 4, 4, 8, 8, 8, 8, 16, 16, 8, 8, 16, 16, 16, 16, 32, 32, 8, 8, 16, 16, 16, 16, 32, 32, 16, 16, 32, 32, 32, 32, 64, 64, 4, 4, 8, 8, 8, 8, 16, 16
Offset: 0

Views

Author

Omar E. Pol, Dec 23 2012

Keywords

Comments

Essentially the first differences of A220494.
First differs from A194441 (and from A220521) at a(12).

Examples

			When written as an irregular triangle begins:
0;
1;
2;
4,4;
4,4,8,8;
4,4,8,8,8,8,16,16;
4,4,8,8,8,8,16,16,8,8,16,16,16,16,32,32;
4,4,8,8,8,8,16,16,8,8,16,16,16,16,32,32,8,8,16,16,...

Links

Crossrefs

Cf. A139250, A139251, A194271, A194701, A194441, A220494, A220497, A220521.
Showing 1-10 of 12 results. Next

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