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

1,2

Links

David Lovler, Table of n, a(n) for n = 1..300

David Lovler, Triples for m up to 100

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.

Example

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],
  ...

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 *)

Prog

(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

Crossrefs

Cf. A338275, A338896.

Sequence in context: A200267 A273308 A105790 * A090682 A011982 A282939

Adjacent sequences: A338892 A338893 A338894 * A338896 A338897 A338898

Keyword

nonn,tabf

Author

David Lovler, Nov 14 2020

Status

approved