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 1-5 of 5 results.

A372614 Number of vertices among all distinct circles that can be constructed from the 3 vertices and the equally spaced 3*n points placed on the sides of an equilateral triangle, using only a compass.

Original entry on oeis.org

6, 87, 481, 1992, 6969, 15409, 35202, 58422, 107677, 159138, 268572, 350860, 557049
Offset: 0

Views

Author

Scott R. Shannon, May 07 2024

Keywords

Comments

A circle is constructed for every pair of the 3 + 3*n points, the first point defines the circle's center while the second the radius distance.

Crossrefs

Cf. A372615 (regions), A372616 (edges), A372617 (k-gons), A372682 (number of circles), A372731, A371373, A354605, A360351.

Formula

a(n) = A372616(n) - A372615(n) + 1 by Euler's formula.

A372615 Number of regions among all distinct circles that can be constructed from the 3 vertices and the equally spaced 3*n points placed on the sides of an equilateral triangle, using only a compass.

Original entry on oeis.org

7, 121, 624, 2368, 7912, 17115, 38461, 63184, 115614, 170149, 285715, 371982, 588043
Offset: 0

Views

Author

Scott R. Shannon, May 07 2024

Keywords

Comments

A circle is constructed for every pair of the 3 + 3*n points, the first point defines the circle's center while the second the radius distance.
The vertices of the initial equilateral triangle are indicated by small circles in the illustrations here.

Crossrefs

Cf. A372614 (vertices), A372616 (edges), A372617 (k-gons), A372682 (number of circles), A371374, A353782, A360352.

Formula

a(n) = A372616(n) - A372614(n) + 1 by Euler's formula.

A372616 Number of curved edges among all distinct circles that can be constructed from the 3 vertices and the equally spaced 3*n points placed on the sides of an equilateral triangle, using only a compass.

Original entry on oeis.org

12, 207, 1104, 4359, 14880, 32523, 73662, 121605, 223290, 329286, 554286, 722841, 1145091
Offset: 0

Views

Author

Scott R. Shannon, May 07 2024

Keywords

Comments

A circle is constructed for every pair of the 3 + 3*n points, the first point defines the circle's center while the second the radius distance.
See A372614 and A372615 for images of the circles.

Crossrefs

Cf. A372614 (vertices), A372615 (regions), A372617 (k-gons), A372682 (number of circles), A371375, A356358, A360353.

Formula

a(n) = A372614(n) + A372615(n) - 1 by Euler's formula.

A372734 Irregular table read by rows: T(n,k) is the number of k-gons, k>=2, among all distinct circles that can be constructed from the 3 vertices and the equally spaced 3*n points placed on the sides of an equilateral triangle when every pair of the 3 + 3*n points are connected by a circle and where the points lie at the ends of the circle's diameter.

Original entry on oeis.org

0, 7, 12, 61, 9, 6, 6, 303, 108, 9, 9, 3, 18, 771, 603, 150, 15, 9, 0, 1, 24, 1722, 1740, 339, 81, 3, 0, 1, 30, 3789, 4326, 1104, 234, 18, 3, 36, 6907, 8274, 2193, 432, 45, 18, 66, 12012, 15504, 4173, 922, 105, 45, 3, 3, 90, 19860, 24774, 7389, 1773, 150, 30, 48, 30594, 39852, 12438, 2998, 387, 48
Offset: 0

Views

Author

Scott R. Shannon, May 12 2024

Keywords

Comments

A circle is constructed for every pair of the 3 + 3*n points, the two points lying at the ends of a diameter of the circle.
See A372731 and A372732 for images of the circles.

Examples

			The table begins:
0, 7;
12, 61, 9, 6;
6, 303, 108, 9, 9, 3;
18, 771, 603, 150, 15, 9, 0, 1;
24, 1722, 1740, 339, 81, 3, 0, 1;
30, 3789, 4326, 1104, 234, 18, 3;
36, 6907, 8274, 2193, 432, 45, 18;
66, 12012, 15504, 4173, 922, 105, 45, 3, 3;
90, 19860, 24774, 7389, 1773, 150, 30;
48, 30594, 39852, 12438, 2998, 387, 48;
96, 45456, 59019, 18669, 4429, 609, 93, 3, 6;
90, 66633, 86088, 29136, 6840, 1164, 195, 6;
120, 90210, 121614, 40035, 9160, 1362, 177, 12, 9;
108, 124245, 167646, 57048, 14377, 1989, 300, 33, 15;
.
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Crossrefs

Cf. A372731 (vertices), A372732 (regions), A372733 (edges), A372735 (number of circles), A372617, A371376, A361623, A360354.

Formula

Sum of row(n) = A372732(n).

A372980 Irregular table read by rows: T(n,k) is the number of k-gons, k>=3, among all distinct circles that can be constructed from the 4 vertices and the equally spaced 4*n points placed on the sides of a square, using only a compass.

Original entry on oeis.org

16, 29, 272, 260, 80, 12, 4, 1708, 2253, 528, 120, 20, 4, 5200, 7636, 2136, 432, 44, 20, 8, 13732, 20788, 5712, 1120, 184, 17, 8, 31576, 49284, 14060, 3180, 584, 108, 16, 64748, 103557, 30372, 6472, 980, 172, 4, 12, 103368, 166804, 49920, 11196, 1660, 260, 48, 16, 181376, 296388, 88916, 19844, 3128, 445, 64, 20
Offset: 0

Views

Author

Scott R. Shannon, May 19 2024

Keywords

Comments

A circle is constructed for every pair of the 4 + 4*n points, the first point defines the circle's center while the second the radius distance.
Unlike A372617, a similar sequence but with vertices on an equilateral triangle, for the terms studied no graph has 2-edged regions.
See A372977 and A372978 for images of the circles.

Examples

			The table begins:
16, 29;
272, 260, 80, 12, 4;
1708, 2253, 528, 120, 20, 4;
5200, 7636, 2136, 432, 44, 20, 8;
13732, 20788, 5712, 1120, 184, 17, 8;
31576, 49284, 14060, 3180, 584, 108, 16;
64748, 103557, 30372, 6472, 980, 172, 4, 12;
103368, 166804, 49920, 11196, 1660, 260, 48, 16;
181376, 296388, 88916, 19844, 3128, 445, 64, 20;
.
.
		

Crossrefs

Cf. A372977 (vertices), A372978 (regions), A372979 (edges), A372981 (circles), A372617, A371376, A361623, A360354.

Formula

Sum of row n = A372978(n).
Showing 1-5 of 5 results.