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.

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A242394 Number of equilateral triangles (sides length = 1) that intersect the circumference of a circle of radius n centered at (0,0).

Original entry on oeis.org

6, 18, 30, 42, 54, 66, 66, 102, 114, 126, 138, 150, 150, 162, 198, 210, 222, 234, 222, 270, 258, 294, 306, 318, 330, 330, 366, 354, 390, 402, 390, 426, 450, 462, 450, 486, 474, 486, 510, 546, 558, 546, 558, 594, 606, 630, 642, 654, 618, 678, 690, 690, 726, 738, 750, 738, 750
Offset: 1

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Author

Kival Ngaokrajang, May 13 2014

Keywords

Comments

For all n, there are at least 6 points where the transit of circumference occurs exactly at the corners. The rare case is when the transit occurs at 2 corners of a triangle, i.e., at n = 1, 13, 181, 35113, ... , (A001570(n)). The pattern repeats itself at every Pi/3 sector along the circumference. The triangle count per half sector by rows can be arranged as an irregular triangle as shown in the illustration. The rows count (A242396) is equal to the case centered at (1/2,0), A242395.

Links

Crossrefs

Cf. A001570, A242118.

A242396 Number of rows of equilateral triangles (sides length = 1) that intersect the circumference of a circle of radius n centered at (0,0) or (1/2,0).

Original entry on oeis.org

4, 6, 8, 10, 12, 14, 18, 20, 22, 24, 26, 28, 32, 34, 36, 38, 40, 42, 44, 48, 50, 52, 54, 56, 58, 62, 64, 66, 68, 70, 72, 74, 78, 80, 82, 84, 86, 88, 92, 94, 96, 98, 100, 102, 104, 108, 110, 112, 114, 116, 118, 122, 124, 126, 128, 130, 132, 134, 138, 140, 142
Offset: 1

Views

Author

Kival Ngaokrajang, May 13 2014

Keywords

Comments

See crossreferenced sequences for illustrations.

Crossrefs

Cf. A242394, A242395.

Formula

G.f., conjectured: (-2*x^14 + 4*x^13 + 2*x^12 + 2*x^11 + 2*x^10 + 2*x^9 + 2*x^8 + 4*x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 4*x)/(x^14 - x^13 - x + 1). - Ralf Stephan, May 18 2014
Asymptotics from g.f.: a(n) ~ 30/13 * n. - Ralf Stephan, May 18 2014

A244147 Number of hexagons (side length 1) that intersect the circumference of a circle of radius n centered at a lattice point.

Original entry on oeis.org

3, 9, 12, 15, 21, 24, 27, 39, 42, 39, 51, 54, 51, 63, 66, 69, 81, 78, 75, 99, 96, 93, 105, 114, 105, 123, 120, 117, 141, 138, 129, 147, 156, 153, 159, 162, 159, 177, 180, 171, 201, 192, 183, 201, 204, 201, 219, 216, 207, 237, 240, 225, 249, 258, 243, 267, 246, 261, 285, 276
Offset: 1

Views

Author

Kival Ngaokrajang, Jun 21 2014

Keywords

Comments

The pattern repeats itself at every 2*Pi/3 sector along the circumference. The hexagon count per one-third sector by rows can be arranged as an irregular triangle. The double hexagons in a row are symmetrically placed. See illustration.

Links

Crossrefs

Cf. A242118, A242394, A242395.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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