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 1-3 of 3 results.

A332978 The number of regions formed inside a triangle with leg lengths equal to the Pythagorean triples by straight line segments mutually connecting all vertices and all points that divide the sides into unit length parts.

Original entry on oeis.org

271, 5746, 14040, 32294, 50551, 108737, 180662, 276533, 259805, 558256, 591687, 901811, 1117126, 1015277, 1386667, 1223260, 1944396, 3149291, 3165147, 4523784, 4764416, 4859839, 6025266, 7186096
Offset: 1

Views

Author

Scott R. Shannon and N. J. A. Sloane, Mar 04 2020

Keywords

Comments

The terms are from numeric computation - no formula for a(n) is currently known.

Examples

			The triples are ordered by the total sum of the leg lengths:
           Triple        |      Number of regions
          (3, 4, 5)      |           271
          (6, 8, 10)     |           5746
          (5, 12, 13)    |           14040
          (9, 12, 15)    |           32294
          (8, 15, 17)    |           50551
          (12, 16, 20)   |           108737
          (7, 24, 25)    |           180662
          (15, 20, 25)   |           276533
          (10, 24, 26)   |           259805
          (20, 21, 29)   |           558256
          (18, 24, 30)   |           591687
          (16, 30, 34)   |           901811
          (21, 28, 35)   |           1117126
          (12, 35, 37)   |           1015277
          (15, 36, 39)   |           1386667
          (9, 40, 41)    |           1223260
          (24, 32, 40)   |           1944396
          (27, 36, 45)   |           3149291
          (14, 48, 50)   |           3165147
          (20, 48, 52)   |           4523784
          (24, 45, 51)   |           4764416
          (30, 40, 50)   |           4859839
          (28, 45, 53)   |           6025266
          (33, 44, 55)   |           7186096

Links

Crossrefs

Cf. A333135 (n-gons), A333136 (vertices), A333137 (edges), A103605 (Pythagorean triple ordering), A007678, A092867, A331452.

Extensions

a(8)-a(24) from Lars Blomberg, Jun 07 2020

A333135 Irregular table read by rows: Take a triangle with Pythagorean triple leg lengths with all diagonals drawn, as in A332978. Then T(n,k) = number of k-sided polygons in that figure for k >= 3 where the legs are divided into unit length parts.

Original entry on oeis.org

139, 94, 34, 3, 1, 2383, 2421, 760, 167, 13, 2, 5307, 5958, 2113, 563, 80, 17, 2, 13083, 13560, 4479, 1002, 153, 16, 1, 18827, 20896, 8256, 2139, 377, 49, 6, 1, 42992, 45400, 15930, 3771, 579, 60, 5, 63526, 79275, 28922, 7315, 1404, 202, 14, 4
Offset: 1

Views

Author

Scott R. Shannon and N. J. A. Sloane, Mar 09 2020

Keywords

Comments

See A332978 for the Pythagorean triple ordering and the links for images of the triangles.

Examples

			Table begins:
139, 94, 34, 3, 1;
2383, 2421, 760, 167, 13, 2;
5307, 5958, 2113, 563, 80, 17, 2;
13083, 13560, 4479, 1002, 153, 16, 1;
18827, 20896, 8256, 2139, 377, 49, 6, 1;
42992, 45400, 15930, 3771, 579, 60, 5;
63526, 79275, 28922, 7315, 1404, 202, 14, 4;
The row sums are A332978.

Links

Crossrefs

Cf. A332978 (regions), A333136 (vertices), A333137 (edges), A103605 (Pythagorean triple ordering), A007678, A092867, A331452.

Extensions

Corrected typo in a(12) and a(49) and beyond from Lars Blomberg, Jun 07 2020

A333136 The number of vertices formed on a triangle with leg lengths equal to the Pythagorean triples by the straight line segments mutually connecting all vertices and all points that divide the sides into unit length parts.

Original entry on oeis.org

230, 5138, 13181, 29277, 48107, 100003, 173261, 256910, 247940, 541752, 554717, 869197, 1051503, 987045, 1333241, 1190131, 1843049, 2991447, 3073340, 4382249, 4630456, 4635744, 5914142, 6877208
Offset: 1

Views

Author

Scott R. Shannon and N. J. A. Sloane, Mar 09 2020

Keywords

Comments

See A332978 for the Pythagorean triple ordering and the links for images of the triangles.

Crossrefs

Cf. A332978 (regions), A333135 (n-gons), A333137 (edges), A103605 (Pythagorean triple ordering), A092866, A332599, A007569.

Extensions

a(8)-a(24) from Lars Blomberg, Jun 07 2020
Showing 1-3 of 3 results.

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

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