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 1-4 of 4 results.

A161336 Snowflake tree sequence: (A161330(n+1) - 2)/6.

Original entry on oeis.org

0, 1, 2, 3, 6, 7, 10, 13, 16, 21, 24, 29, 36, 37, 40, 43, 48, 57, 62, 75, 82, 91, 104, 111, 122, 135, 138, 145, 152, 161, 176, 187, 208, 223, 238, 255, 266, 279, 294, 309, 324, 333, 344, 363, 376, 397, 418, 435, 452, 475, 492, 519, 536, 555, 582, 603, 630, 649, 666, 683
Offset: 0

Views

Author

Omar E. Pol, Jun 09 2009

Keywords

Comments

This is an E-toothpick sequence. On a triangular graph paper consider an infinite 60-degree wedge in which there is a single (and virtual) toothpick connected to its vertex. At stage 0 we start with no E-toothpicks. At stage 1 we place an E-toothpick, and so on. The sequence gives the number of E-toothpicks in the structure after n stages. A211974 (the first differences) gives the number added at the n-th stage. The structure is the tree that arise from one of the six spokes of the structure of A213360 which is essentially the same as the E-toothpick (or snowflake) structure of A161330. For n >> 1 the structure looks like a quadrilateral formed by two scalene right triangles which are joined at their hypotenuses. - Omar E. Pol, Dec 19 2012

Links

Crossrefs

Cf. A139250, A161328, A161330, A161337, A161338, A211974, A213360.

Formula

a(n) = A213360(n)/6. - Omar E. Pol, Dec 20 2012

Extensions

Extended and edited by Omar E. Pol, Dec 19 2012

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.
Showing 1-4 of 4 results.

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