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.

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

1,1

Comments

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

Links

Table of n, a(n) for n=1..24.

Scott R. Shannon, Triangle regions for leg lengths (3,4,5).

Scott R. Shannon, Triangle regions for leg lengths (6,8,10).

Scott R. Shannon, Triangle regions for leg lengths (5,12,13).

Scott R. Shannon, Triangle regions for leg lengths (9,12,15).

Scott R. Shannon, Triangle regions for leg lengths (8,15,17).

Eric Weisstein's World of Mathematics, Pythagorean Triple.

Wikipedia, Pythagorean triple.

Example

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

Crossrefs

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

Sequence in context: A185668 A296038 A287232 * A214012 A303886 A305279

Adjacent sequences: A332975 A332976 A332977 * A332979 A332980 A332981

Keyword

nonn,more

Author

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

Extensions

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

Status

approved