A338895 Three-column table read by rows giving Pythagorean triples [a,b,c] that are the (constant) differences between consecutive triples in rows of A338275.

0, 4, 4, 6, 8, 10, 0, 16, 16, 16, 12, 20, 10, 24, 26, 0, 36, 36, 30, 16, 34, 24, 32, 40, 14, 48, 50, 0, 64, 64, 48, 20, 52, 42, 40, 58, 32, 60, 68, 18, 80, 82, 0, 100, 100, 70, 24, 74, 64, 48, 80, 54, 72, 90, 40, 96, 104, 22, 120, 122, 0, 144, 144

Offset: 1

Author

David Lovler, Nov 14 2020

Keywords

• nonn
• tabf

Examples

			The table begins:
  [ 0,   4,   4],
  [ 6,   8,  10],
  [ 0,  16,  16],
  [16,  12,  20],
  [10,  24,  26],
  [ 0,  36,  36],
  [30,  16,  34],
  [24,  32,  40],
  [14,  48,  50],
  [ 0,  64,  64],
  [48,  20,  52],
  [42,  40,  58],
  [32,  60,  68],
  [18,  80,  82],
  [ 0, 100, 100],
  [70,  24,  74],
  [64,  48,  80],
  [54,  72,  90],
  [40,  96, 104],
  [22, 120, 122],
  [ 0, 144, 144],
  ...
		

Links

• David Lovler, Table of n, a(n) for n = 1..300
• David Lovler, Triples for m up to 100

Crossrefs

Cf. A338275, A338896.

Programs

Mathematica

Table[{((#1 - 1)^2 - #2^2)/2, (#1 - 1) #2, ((#1 - 1)^2 + #2^2)/2} & @@ {m, n}, {m, 3, 13, 2}, {n, 2, m, 2}] // Flatten (* Michael De Vlieger, Dec 04 2020 *)

PARI

lista(mm) = {forstep (m=3, mm, 2, forstep (n=2, m, 2, print([((m-1)^2 - n^2)/2, (m-1)*n, ((m-1)^2 + n^2)/2]);););} \\ Michel Marcus, Dec 04 2020

Formula

a = ((m-1)^2 - n^2)/2, b = (m-1)*n, c = ((m-1)^2 + n^2)/2, where m and n generate the A338275 row in question.