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.

Previous Showing 11-19 of 19 results.

A161412 V-toothpick sequence starting at the corner of an infinite square from which protrudes a half toothpick with an angle = Pi/6.

Original entry on oeis.org

0, 1, 2, 3, 5, 9, 12, 15, 19, 25, 29, 34, 39, 49, 58, 63
Offset: 0

Views

Author

Omar E. Pol, Jun 10 2009

Keywords

Comments

The sequence gives the number of V-toothpicks in the structure after n rounds. A161413 (the first differences) gives the number added at the n-th round.

Links

Crossrefs

V-toothpick sequence: A161206.
Cf. A139250, A160120, A160406, A161328, A161413.

A213360 Snowflake sequence starting with six E-toothpicks.

Original entry on oeis.org

0, 6, 12, 18, 36, 42, 60, 78, 96, 126, 144, 174, 216, 222, 240, 258, 288, 342, 372, 450, 492, 546, 624, 666, 732, 810, 828, 870, 912, 966, 1056, 1122, 1248, 1338, 1428, 1530, 1596, 1674, 1764, 1854, 1944, 1998, 2064, 2178, 2256, 2382, 2508, 2610, 2712, 2850, 2952, 3114, 3216, 3330, 3492, 3618, 3780, 3894, 3996, 4098
Offset: 0

Views

Author

Omar E. Pol, Dec 16 2012

Keywords

Comments

The structure is the same as A161330 but without the two central E-toothpicks. All terms are multiples of 6.

Links

Crossrefs

Cf. A008588, A139250, A161328, A161330, A161336.

Formula

a(n) = A161330(n+1) - 2 = 6*A161336(n).

A161334 Numbers of snowflake sequence, divided by 2: a(n) = A161330(n)/2.

Original entry on oeis.org

0, 1, 4, 7, 10, 19, 22, 31, 40, 49, 64, 73, 88, 109, 112, 121, 130, 145, 172, 187, 226, 247, 274, 313, 334, 367, 406, 415, 436, 457, 484, 529, 562, 625, 670, 715, 766, 799, 838, 883, 928, 973, 1000, 1033, 1090, 1129, 1192, 1255, 1306, 1357, 1426, 1477
Offset: 0

Views

Author

Omar E. Pol, Jun 07 2009

Keywords

Comments

Also number of E-toothpicks after n-th stage on the semi-infinite triangular grid. A161332 (the first differences) gives the number of E-toothpicks added at n-th stage. - Omar E. Pol, Jan 07 2014

Links

Crossrefs

Cf. A139250, A161328, A161330, A161331, A161332, A161333.

Extensions

More terms from Omar E. Pol, Jan 07 2014

A161420 V-toothpick sequence starting from a V-toothpick whose central point touch a straight line, as a V.

Original entry on oeis.org

0, 1, 3, 5, 7, 11, 19, 25, 31, 39, 51, 59, 69, 79, 99, 117, 127, 143, 163, 171
Offset: 0

Views

Author

Omar E. Pol, Jun 10 2009

Keywords

Comments

The sequence gives the number of V-toothpicks after n-th stages on hexagonal net. A161421 (the first differences) gives the number added at the n-th stage. See A161206 for more information.
Also, it appears this is a H-toothpick sequence in the first quadrant on the square grid, starting with a D-toothpick from the point (0,0). The sequence gives the number of toothpicks and D-toothpicks after n-th stage. A161421 (the first differences) gives the number added at the n-th stage. For more information see A182838.

Links

Crossrefs

Cf. A139250, A160120, A160406, A161206, A161328, A161412, A161421, A161422, A161423, A182832, A182838.

A220478 Equilateral triangle from the snowflake (or E-toothpick) structure of A161330 (see Comments lines for definition).

Original entry on oeis.org

0, 2, 4, 6, 10, 12, 16, 20, 24, 30, 34, 40, 48, 50, 54, 58, 64, 74, 80, 94, 102, 112, 126, 134, 146, 160, 164, 172, 180, 190, 206, 218, 240, 256, 272, 290, 302, 316, 332, 348, 364, 374, 386, 406, 420, 442, 464, 482, 500, 524, 542, 570, 588, 608, 636, 658, 686, 706, 724, 742
Offset: 0

Views

Author

Omar E. Pol, Dec 22 2012

Keywords

Comments

It appears that if n >> 1 the structure looks like an equilateral triangle, which is essentially one of the six wedges of the E-toothpick (or snowflake) structure of A161330. The sequence gives the number of E-toothpicks in the structure after n stages. A220498 (the first differences) gives the number added at the n-th round. For more information and some illustrations see A161330. For the E-toothpick right triangle see A211964.

Links

Crossrefs

Cf. A139250, A161328, A160120, A161330, A161336, A211964, A213360, A220498.

Formula

a(n) = n + (A161330(n) - 2)/6, n >= 1.
a(n) = n + A161336(n) = 2*A211964(n).

A211964 Right triangle from the snowflake (or E-toothpick) structure of A161330 (see Comments lines for definition).

Original entry on oeis.org

0, 1, 2, 3, 5, 6, 8, 10, 12, 15, 17, 20, 24, 25, 27, 29, 32, 37, 40, 47, 51, 56, 63, 67, 73, 80, 82, 86, 90, 95, 103, 109, 120, 128, 136, 145, 151, 158, 166, 174, 182, 187, 193, 203, 210, 221, 232, 241, 250, 262, 271, 285, 294, 304, 318, 329, 343, 353, 362, 371
Offset: 0

Views

Author

Omar E. Pol, Dec 17 2012

Keywords

Comments

If n >> 1 the structure looks like a right triangle, which is essentially half of one of the six wedges of the E-toothpick (or snowflake) structure of A161330. The sequence gives the number of E-toothpicks in the structure after n stages. A211976 (the first differences) gives the number added at the n-th stage.

Links

Crossrefs

Cf. A139250, A161328, A161330, A213360, A213366, A211976, A220478.

Formula

a(n) = (((A161330(n+1) - 2)/6) + n)/2.
a(n) = A220478(n)/2. - Omar E. Pol, Feb 19 2012

A211974 Number of E-toothpicks added at n-th stage in the structure of A161336.

Original entry on oeis.org

0, 1, 1, 1, 3, 1, 3, 3, 3, 5, 3, 5, 7, 1, 3, 3, 5, 9, 5, 13, 7, 9, 13, 7, 11, 13, 3, 7, 7, 9, 15, 11, 21, 15, 15, 17, 11, 13, 15, 15, 15, 9, 11, 19, 13, 21, 21, 17, 17, 23, 17, 27, 17, 19, 27, 21, 27, 19, 17, 17, 21, 31, 31, 25, 23
Offset: 0

Views

Author

Omar E. Pol, Dec 15 2012

Keywords

Comments

Essentially the first differences of A161336.

Links

Crossrefs

Cf. A139250, A139251, A161328, A161330, A213360, A211976.

Formula

a(n) = A161331(n+1)/6, n >= 1.

A294960 Snowflake (or E-toothpick) sequence of the second kind (see Comments lines for definition).

Original entry on oeis.org

0, 2, 8, 14, 20, 26, 44, 50, 68, 86, 104, 110, 128, 158, 176, 206, 260, 278, 320, 350, 392, 410, 452, 494, 548, 614
Offset: 0

Views

Author

Omar E. Pol, Nov 12 2017

Keywords

Comments

This has essentially the same rules as the snowflake sequence A161330, but here there is an additional rule: there are no E-toothpicks of the same generation that share the endpoint of two parallel components.
The structure is lighter than the structure of A161330 from which differs at a(7).
Note that, on the infinite triangular grid, an E-toothpick can be represented as a polyedge with three components. In this case, at the n-th round, the structure is a polyedge with 3*a(n) components.
An E-toothpick looks like a bird's footprint (or more generally a dinosaur's footprint).
a(n) gives the number of E-toothpicks in the structure after n rounds.
A294961(n) is the number of E-toothpicks added at the n-th round, n >= 1. - Omar E. Pol, Apr 15 2018

Links

Crossrefs

Another version of A161330.
Cf. A139250, A160120, A161328, A294961 (first differences).

A294961 a(n) is the number of E-toothpicks added at n-th stage in the structure of the snowflake cellular automaton of A294960.

Original entry on oeis.org

2, 6, 6, 6, 6, 18, 6, 18, 18, 18, 6, 18, 30, 18, 30, 54, 18, 42, 30, 42, 18, 42, 42, 54, 66
Offset: 1

Views

Author

Omar E. Pol, Feb 10 2018

Keywords

Links

Crossrefs

First differences of A294960.
Cf. A139251, A161328, A161329, A161330, A161331.
Previous Showing 11-19 of 19 results.

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