A242394 -id:A242394 - cp's OEIS frontend

A242395 Number of equilateral triangles (sides length = 1) that intersect the circumference of a circle of radius n centered at (1/2,0).

14, 26, 38, 58, 70, 82, 98, 110, 122, 142, 154, 166, 182, 194, 206, 218, 238, 250, 262, 278, 290, 302, 322, 334, 346, 362, 374, 386, 398, 418, 430, 442, 458, 470, 482, 502, 514, 526, 542, 554, 566, 578, 598, 610, 622, 638, 650, 662, 682, 694, 706, 722, 734, 746, 766, 778, 790

Offset: 1

Kival Ngaokrajang, May 13 2014

nonn

For all n, it seems to be the case that transits of the circumference occurring exactly at the corners do not exist. The pattern repeats itself at a half circle. The triangle count in a quadrant 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 (0,0), A242394.

Kival Ngaokrajang, Illustration of initial terms

Cf. 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

Kival Ngaokrajang, May 13 2014

nonn

See crossreferenced sequences for illustrations.

Cf. A242394, A242395.

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

Kival Ngaokrajang, Jun 21 2014

nonn

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.

Kival Ngaokrajang, Illustration of initial terms
Kival Ngaokrajang, Small Basic program

Cf. A242118, A242394, A242395.

cp's OEIS Frontend

A242395 Number of equilateral triangles (sides length = 1) that intersect the circumference of a circle of radius n centered at (1/2,0).

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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).

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

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