A332978 - OEIS

%I #30 Jun 07 2020 10:20:00

%S 271,5746,14040,32294,50551,108737,180662,276533,259805,558256,591687,

%T 901811,1117126,1015277,1386667,1223260,1944396,3149291,3165147,

%U 4523784,4764416,4859839,6025266,7186096

%N 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.

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

%H Scott R. Shannon, <a href="/A332978/a332978.png">Triangle regions for leg lengths (3,4,5)</a>.

%H Scott R. Shannon, <a href="/A332978/a332978_3.png">Triangle regions for leg lengths (6,8,10)</a>.

%H Scott R. Shannon, <a href="/A332978/a332978_1.png">Triangle regions for leg lengths (5,12,13)</a>.

%H Scott R. Shannon, <a href="/A332978/a332978_4.png">Triangle regions for leg lengths (9,12,15)</a>.

%H Scott R. Shannon, <a href="/A332978/a332978_2.png">Triangle regions for leg lengths (8,15,17)</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PythagoreanTriple.html">Pythagorean Triple</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Pythagorean_triple">Pythagorean triple</a>.

%e The triples are ordered by the total sum of the leg lengths:

%e            Triple        |      Number of regions

%e           (3, 4, 5)      |           271

%e           (6, 8, 10)     |           5746

%e           (5, 12, 13)    |           14040

%e           (9, 12, 15)    |           32294

%e           (8, 15, 17)    |           50551

%e           (12, 16, 20)   |           108737

%e           (7, 24, 25)    |           180662

%e           (15, 20, 25)   |           276533

%e           (10, 24, 26)   |           259805

%e           (20, 21, 29)   |           558256

%e           (18, 24, 30)   |           591687

%e           (16, 30, 34)   |           901811

%e           (21, 28, 35)   |           1117126

%e           (12, 35, 37)   |           1015277

%e           (15, 36, 39)   |           1386667

%e           (9, 40, 41)    |           1223260

%e           (24, 32, 40)   |           1944396

%e           (27, 36, 45)   |           3149291

%e           (14, 48, 50)   |           3165147

%e           (20, 48, 52)   |           4523784

%e           (24, 45, 51)   |           4764416

%e           (30, 40, 50)   |           4859839

%e           (28, 45, 53)   |           6025266

%e           (33, 44, 55)   |           7186096

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

%K nonn,more

%O 1,1

%A _Scott R. Shannon_ and _N. J. A. Sloane_, Mar 04 2020

%E a(8)-a(24) from _Lars Blomberg_, Jun 07 2020