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 1-10 of 10 results.

A067167 A067155(n)/n.

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 1, 0, 2, 1, 0, 2, 1, 4, 1, 5, 0, 7, 0, 8, 3, 9, 2, 11, 5, 14, 5, 16, 1, 21, 12, 18, 13, 25, 6, 22, 11, 29, 15, 22, 9, 31, 14, 43, 22, 52, 16, 52, 30, 69, 38, 65, 36, 74, 44, 51, 34, 58, 36, 95, 37, 68, 48, 87, 54, 92, 48, 96, 63, 92, 52, 110, 80, 133
Offset: 9

Views

Author

Sascha Kurz, Jan 06 2002

Keywords

References

  • B. Poonen and M. Rubinstein, Number of Intersection Points Made by the Diagonals of a Regular Polygon, SIAM J. Discrete Mathematics, Vol. 11, pp. 135-156.

Links

Crossrefs

Cf. A067155.

A067151 Number of regions in regular n-gon which are quadrilaterals (4-gons) when all its diagonals are drawn.

Original entry on oeis.org

0, 0, 6, 7, 24, 36, 90, 132, 168, 234, 378, 600, 672, 901, 954, 1444, 1580, 2520, 2860, 2990, 3696, 4800, 5070, 6750, 7644, 9309, 7920, 12927, 12896, 15576, 16898, 20475, 18684, 25382, 27246, 30966, 32760, 37064, 37170, 45838, 47300, 55350, 60996, 69231, 66864, 80507, 87550, 98124, 103272
Offset: 4

Views

Author

Sascha Kurz, Jan 06 2002

Keywords

Examples

			a(6)=6 because the 6 regions around the center are quadrilaterals.

References

  • B. Poonen and M. Rubinstein, Number of Intersection Points Made by the Diagonals of a Regular Polygon, SIAM J. Discrete Mathematics, Vol. 11, pp. 135-156.

Links

Crossrefs

Cf. A007678, A067163, A064869, A067152, A067153, A067154, A067155, A067156, A067157, A067158, A067159.

Formula

Conjecture: a(n) ~ c * n^4. Is c = 1/64 ? - Bill McEachen, Mar 03 2024

Extensions

Title clarified, a(47) and above by Scott R. Shannon, Dec 04 2021

A067152 Number of pentagonal regions in regular n-gon with all diagonals drawn.

Original entry on oeis.org

1, 0, 7, 0, 18, 10, 44, 0, 117, 98, 150, 128, 357, 72, 646, 580, 903, 814, 1564, 840, 2050, 2106, 2862, 2128, 3625, 1440, 5146, 4896, 6105, 5542, 8190, 7452, 10471, 10184, 14235, 13160, 16564, 11382, 21156, 20548, 24300, 23920, 30362, 26112, 35231, 32700, 40341, 38532, 51834, 42012, 58905
Offset: 5

Views

Author

Sascha Kurz, Jan 06 2002

Keywords

Examples

			a(5) = 1 because only the center-region is a pentagon.

References

  • B. Poonen and M. Rubinstein, Number of Intersection Points Made by the Diagonals of a Regular Polygon, SIAM J. Discrete Mathematics, Vol. 11, pp. 135-156.

Links

Crossrefs

Cf. A007678, A067164, A064869, A067151, A067153, A067154, A067155, A067156, A067157, A067158, A067159.

Extensions

a(49) and beyond from Scott R. Shannon, Dec 04 2021
Definition clarified by N. J. A. Sloane, Jun 09 2025

A067153 Number of hexagonal regions in regular n-gon with all diagonals drawn.

Original entry on oeis.org

0, 0, 0, 9, 0, 22, 0, 39, 0, 105, 48, 136, 18, 190, 120, 462, 66, 644, 72, 875, 390, 1296, 952, 1595, 450, 1891, 1472, 3201, 2346, 3640, 2124, 4773, 2698, 5577, 4000, 7298, 3444, 7912, 6336, 10980, 6532, 10904, 7824, 14651, 12150, 16779, 13260, 20299, 13176, 21560, 18200, 26961, 21634, 29500
Offset: 6

Views

Author

Sascha Kurz, Jan 06 2002

Keywords

Examples

			a(9)=9 because drawing the regular 9-gon with all its diagonals yields 9 hexagons.

References

  • B. Poonen and M. Rubinstein, Number of Intersection Points Made by the Diagonals of a Regular Polygon, SIAM J. Discrete Mathematics, Vol. 11, pp. 135-156.

Links

Crossrefs

Cf. A007678, A067165, A064869, A067151, A067152, A067154, A067155, A067156, A067157, A067158, A067159.

Extensions

a(54) and beyond from Scott R. Shannon, Dec 04 2021
Definition clarified by N. J. A. Sloane, Jun 09 2025

A067154 Number of heptagonal regions in regular n-gon with all diagonals drawn.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 0, 15, 0, 17, 18, 57, 0, 21, 44, 115, 0, 150, 104, 81, 112, 116, 0, 155, 224, 429, 306, 560, 180, 555, 836, 663, 640, 1025, 378, 1419, 660, 1710, 1564, 1786, 1200, 2352, 1050, 2754, 2236, 2597, 2700, 3410, 2240, 3078, 3190, 4602, 1860, 5551, 4898, 6363, 5056, 8515, 4950
Offset: 7

Views

Author

Sascha Kurz, Jan 06 2002

Keywords

Examples

			a(7)=1 because the center-region is a heptagon.

References

  • B. Poonen and M. Rubinstein, Number of Intersection Points Made by the Diagonals of a Regular Polygon, SIAM J. Discrete Mathematics, Vol. 11, pp. 135-156.

Links

Crossrefs

Cf. A007678, A067166, A064869, A067151, A067152, A067153, A067155, A067156, A067157, A067158, A067159.

Extensions

a(62) and beyond from Scott R. Shannon, Dec 04 2021
Definition clarified by N. J. A. Sloane, Jun 09 2025

A067156 Number of regions in regular n-gon which are 9-gons.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35, 0, 0, 0, 0, 0, 123, 0, 0, 88, 45, 0, 0, 0, 0, 0, 51, 0, 0, 0, 165, 0, 114, 0, 118, 120, 61, 124, 0, 192, 195, 66, 67, 272, 138, 0, 568, 360, 146, 222, 600, 0, 231, 156, 237, 800, 567, 410, 664, 84, 255, 344, 174
Offset: 9

Views

Author

Sascha Kurz, Jan 06 2002

Keywords

Examples

			a(9)=1 because drawing the regular 9-gon with all its diagonals yields 1 9-gon.

References

  • B. Poonen and M. Rubinstein, Number of Intersection Points Made by the Diagonals of a Regular Polygon, SIAM J. Discrete Mathematics, Vol. 11, pp. 135-156.

Links

Crossrefs

Cf. A007678, A067168, A064869, A067151, A067152, A067153, A067154, A067155, A067157, A067158, A067159.

Extensions

a(86) and beyond by Scott R. Shannon, Dec 04 2021

A067157 Number of regions in regular n-gon which are 10-gons.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 87, 0, 62, 0, 0, 0, 0, 0, 74, 0, 0, 0, 41, 0, 0, 44, 0, 0, 235, 48, 147, 100, 51, 0, 159, 54, 110, 56, 114, 58, 177, 0, 183, 62, 378, 256, 195, 0, 134, 136, 621, 210, 71, 144, 438, 222, 750, 76, 385, 78, 1185, 80, 648, 82, 830, 336, 935
Offset: 10

Views

Author

Sascha Kurz, Jan 06 2002

Keywords

Examples

			a(29)=87 because drawing the regular 29-gon with all its diagonals yields 87 10-gons.

References

  • B. Poonen and M. Rubinstein, Number of Intersection Points Made by the Diagonals of a Regular Polygon, SIAM J. Discrete Mathematics, Vol. 11, pp. 135-156.

Links

Crossrefs

Cf. A007678, A067169, A064869, A067151, A067152, A067153, A067154, A067155, A067156, A067158, A067159.

Extensions

a(83) and beyond by Scott R. Shannon, Dec 04 2021

A067158 Number of regions in regular n-gon which are 11-gons.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 29, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 71, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 99, 0, 0, 102, 103, 0, 0, 0, 0, 108, 0
Offset: 11

Views

Author

Sascha Kurz, Jan 06 2002

Keywords

Examples

			a(11)=1 because drawing the regular 11-gon with all its diagonals yields 1 11-gon.

References

  • B. Poonen and M. Rubinstein, Number of Intersection Points Made by the Diagonals of a Regular Polygon, SIAM J. Discrete Mathematics, Vol. 11, pp. 135-156.

Links

Crossrefs

Cf. A007678, A064869, A067151, A067152, A067153, A067154, A067155, A067156, A067157, A067159.

Extensions

a(110) and beyond by Scott R. Shannon, Dec 04 2021

A067159 Number of regions in regular n-gon which are 12-gons.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 51, 0, 53, 0, 0, 0, 0, 0, 59, 0, 61, 0, 63, 0, 65, 0, 0, 0, 0, 0, 0, 0, 73, 0, 225, 76, 0, 0, 0, 0, 0, 0, 0, 0, 170, 0, 0, 0, 0, 0, 273, 0, 93, 0, 95, 0, 97, 0, 0, 0, 101, 102, 412
Offset: 12

Views

Author

Sascha Kurz, Jan 06 2002

Keywords

Examples

			a(40)=40 because drawing the regular 40-gon with all its diagonals yields 40 12-gons.

References

  • B. Poonen and M. Rubinstein, Number of Intersection Points Made by the Diagonals of a Regular Polygon, SIAM J. Discrete Mathematics, Vol. 11, pp. 135-156.

Links

Crossrefs

Cf. A007678, A064869, A067151, A067152, A067153, A067154, A067155, A067156, A067157, A067158.

Extensions

a(104) and beyond by Scott R. Shannon, Dec 04 2021

A187782 Number of different kinds of polygons in a regular n-gon with all diagonals drawn.

Original entry on oeis.org

1, 1, 2, 2, 4, 2, 5, 3, 5, 2, 6, 3, 6, 4, 7, 5, 7, 5, 6, 6, 7, 4, 7, 6, 7, 6, 9, 4, 8, 5, 7, 6, 8, 6, 8, 6, 7, 7, 9, 6, 8, 8, 8, 6, 8, 7, 8, 7, 10, 6, 9, 7, 9, 7, 9, 7, 10, 7
Offset: 3

Views

Author

Martin Renner, Jan 05 2013

Keywords

Examples

			a(5) = 2 since the 11 regions of the regular pentagon built by all diagonals consist of two different kinds of polygons, i.e., 10 triangles and 1 pentagon.
a(6) = 2 since the 24 regions of the regular hexagon built by all diagonals consist of two different kinds of polygons, i.e., 18 triangles and 6 quadrilaterals.
a(7) = 4 since the 50 regions of the regular heptagon built by all diagonals consist of four different kinds of polygons, i.e., 35 triangles, 7 quadrilaterals, 7 pentagons and 1 heptagon.

Links

Crossrefs

Cf. A007678, A062361, A067151, A067152, A067153, A067154, A067155, A067156, A067157, A067158, A067159.

Extensions

a(45)-a(60) from Christopher Scussel, Jun 24 2023
Showing 1-10 of 10 results.

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