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 1-8 of 8 results.

A353782 Number of regions among all distinct circles that can be constructed from a point on the origin and n equally spaced points on each of the +x,-x,+y,-y coordinates axes using only a compass.

Original entry on oeis.org

112, 1264, 5548, 14976, 37092, 77096, 143560, 237504
Offset: 1

Views

Author

Scott R. Shannon, Mar 13 2023

Keywords

Comments

A circle is constructed for every pair of the 1 + 4n points, the first point defines the circle's center while the second the radius distance. The number of distinct circles constructed from the points is A361622(n).
No formula for a(n) is currently known.

Links

Crossrefs

Cf. A354605 (vertices), A356358 (edges), A361623 (k-gons), A361622 (distinct circles), A359933, A359860, A359253, A359570, A359046.

Formula

a(n) = A356358 - A354605(n) + 1 by Euler's formula.

A359252 Number of vertices among all distinct circles that can be constructed from n equally spaced points along a line using only a compass.

Original entry on oeis.org

2, 13, 46, 101, 226, 417, 744, 1169, 1802, 2599, 3742, 5139, 7022, 9261, 12110, 15367, 19456, 24117, 29858, 36323, 43950, 52595, 62784, 73931, 86806, 101059, 117364, 135155, 155506
Offset: 2

Views

Author

Scott R. Shannon, Dec 22 2022

Keywords

Comments

A circle is constructed for every pair of the n points, the first point defines the circle's center while the second the radius distance. The number of distinct circles constructed for n points is A001859(n-1).
No formula for a(n) is currently known.

Links

Crossrefs

Cf. A359253 (regions), A359254 (edges), A359258 (k-gons), A001859, A290447, A331702, A358746.

Formula

a(n) = A359254(n) - A359253(n) + 1 by Euler's formula.

A359258 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 n equally spaced points along a line using only a compass.

Original entry on oeis.org

3, 0, 8, 4, 2, 0, 22, 23, 4, 2, 0, 50, 52, 12, 2, 0, 110, 103, 36, 6, 0, 190, 200, 64, 12, 0, 314, 387, 88, 28, 4, 0, 498, 606, 152, 32, 8, 0, 770, 941, 228, 58, 4, 2, 0, 1132, 1352, 338, 68, 12, 2, 0, 1602, 1935, 532, 98, 4, 0, 2122, 2798, 684, 106, 16, 0, 2850, 3843, 940, 132, 24, 6
Offset: 2

Views

Author

Scott R. Shannon, Dec 23 2022

Keywords

Comments

A circle is constructed for every pair of the n points, the first point defines the circle's center while the second the radius distance. The number of distinct circles constructed for n points is A001859(n-1).
See A359252 and A359253 for other images of the circles.

Examples

			The table begins:
  3;
  0,     8,     4,    2;
  0,    22,    23,    4,   2;
  0,    50,    52,   12,   2;
  0,   110,   103,   36,   6;
  0,   190,   200,   64,  12;
  0,   314,   387,   88,  28,  4;
  0,   498,   606,  152,  32,  8;
  0,   770,   941,  228,  58,  4,  2;
  0,  1132,  1352,  338,  68, 12,  2;
  0,  1602,  1935,  532,  98,  4;
  0,  2122,  2798,  684, 106, 16;
  0,  2850,  3843,  940, 132, 24,  6;
  0,  3774,  4998, 1268, 192, 28,  6;
  0,  4950,  6475, 1644, 276, 44, 10;
  0,  6190,  8454, 1978, 326, 74,  4;
  0,  7778, 10737, 2520, 434, 52, 12, 4;
  0,  9674, 13224, 3202, 528, 58, 12, 4;
  0, 11978, 16169, 4116, 640, 68, 20, 4;
  ...

Links

Crossrefs

Cf. A359253 (regions), A359252 (vertices), A359254 (edges), A001859, A332723, A359061, A359009.

Formula

Sum of row n = A359253(n);

A359570 Number of regions after n iterations of constructing circles from all current vertices using only a compass, starting with one vertex. See the Comments.

Original entry on oeis.org

0, 1, 3, 21, 7169
Offset: 1

Views

Author

Scott R. Shannon, Jan 06 2023

Keywords

Comments

See A359569 for further details and images.

Links

Crossrefs

Cf. A359569 (vertices), A359571 (edges), A359619 (k-gons), A359253, A359046, A358782.

Formula

For n >= 3, a(n) = A359571(n) - A359569(n) + 1 by Euler's formula.

A359254 Number of edges among all distinct circles that can be constructed from n equally spaced points along a line using only a compass.

Original entry on oeis.org

4, 26, 96, 216, 480, 882, 1564, 2464, 3804, 5502, 7912, 10864, 14816, 19526, 25508, 32392, 40992, 50818, 62852, 76432, 92460, 110590, 131904, 155306, 182316, 212188, 246316, 283586, 326100
Offset: 2

Views

Author

Scott R. Shannon, Dec 22 2022

Keywords

Comments

A circle is constructed for every pair of the n points, the first point defines the circle's center while the second the radius distance. The number of distinct circles constructed for n points is A001859(n-1).
See A359252 and A359253 for images of the circles.

Crossrefs

Cf. A359252 (vertices), A359253 (regions), A359258 (k-gons), A001859, A290866, A359047, A358783.

Formula

a(n) = A359252(n) + A359253(n) - 1 by Euler's formula.

A359933 Number of regions among all distinct circles that can be constructed from an n X n square grid of points using only a compass.

Original entry on oeis.org

45, 836, 8197, 43252, 167157, 535572
Offset: 2

Views

Author

Scott R. Shannon, Jan 21 2023

Keywords

Comments

A circle is constructed for every pair of the n X n points; the first point defines the circle's center while the second defines the radius. The number of distinct circles constructed from the n X n points is A359931(n).
No formula for a(n) is known.

Links

Crossrefs

Cf. A359932 (vertices), A359934 (edges), A359935 (k-gons), A359931 (distinct circles), A359860, A359253.

Formula

a(n) = A359934(n) - A359932(n) + 1 by Euler's formula.

A371253 Number of regions formed when n equally spaced points are placed around a circle and all pairs of points are joined by an interior arc whose radius equals the circle's radius.

Original entry on oeis.org

1, 1, 6, 5, 26, 18, 99, 89, 270, 271, 650, 516, 1288, 1303, 2250, 2337, 4047, 3636, 6404, 6401, 9597, 9769, 14261, 13632, 20251, 20125, 27594, 27749, 37324, 35040, 49043, 49185, 63228, 63547, 80676, 79380, 101640, 102259, 125853, 126561
Offset: 1

Views

Author

Scott R. Shannon, Mar 16 2024

Keywords

Comments

See A371254 for further information.

Links

Crossrefs

Cf. A371254 (vertices), A371255 (edges), A371274 (k-gons), A370980 (number of circles), A371374 (complete circles), A006533, A358782, A359046, A359253, A007678.

Formula

a(n) = A371255(n) - A371254(n) + 1 by Euler's formula.

A359860 Number of regions among all distinct circles that can be constructed from a 2 X n square grid of points using only a compass.

Original entry on oeis.org

3, 45, 231, 865, 2081, 4489, 8211, 14401, 22857, 35445, 51741, 74397, 102271, 138801, 182739, 238181, 303175, 383097, 474995, 586021, 712003, 860829, 1028225, 1223773, 1440593, 1689993, 1965525, 2279509, 2622993, 3011405, 3433615, 3907241, 4419261, 4988781, 5603271
Offset: 1

Views

Author

Scott R. Shannon, Jan 16 2023

Keywords

Comments

See A359859 for further details. No formula for a(n) is known.

Links

Crossrefs

Cf. A359859 (vertices), A359861 (edges), A359862 (k-gons), A001859, A359253.

Formula

a(n) = A359861(n) - A359859(n) + 1 by Euler's formula.

Extensions

a(19)-a(35) from Lucas A. Brown, Oct 11 2024
Showing 1-8 of 8 results.

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