A370777 Table read by rows: row n is the unique primitive Pythagorean quadruple (a,b,c,d) such that (a+b+c-d)/2 = n and a+c=d.

1, 2, 2, 3, 1, 4, 8, 9, 1, 6, 18, 19, 1, 8, 32, 33, 1, 10, 50, 51, 1, 12, 72, 73, 1, 14, 98, 99, 1, 16, 128, 129, 1, 18, 162, 163, 1, 20, 200, 201, 1, 22, 242, 243, 1, 24, 288, 289, 1, 26, 338, 339, 1, 28, 392, 393, 1, 30, 450, 451, 1, 32, 512, 513, 1, 34, 578, 579, 1, 36, 648, 649, 1, 38, 722, 723, 1, 40, 800, 801

Offset

1,2

Comments

A Pythagorean quadruple is a quadruple (a,b,c,d) of positive integers such that a^2 + b^2 + c^2 = d^2 with a <= b <= c. Its inradius is (a+b+c-d)/2, which is a positive integer.

References

Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2024.

Links

Table of n, a(n) for n=1..80.

Miguel-Ángel Pérez García-Ortega, Cuaternas pitagóricas

Formula

Row n = (a, b, c, d) = (1, 2*n, 2*n^2, 2*n^2 + 1).

Example

Table begins:
  n=1:   1,   2,   2,   3;
  n=2:   1,   4,   8,   9;
  n=3:   1,   6,  18,  19;
  n=4:   1,   8,  32,  33;
  n=5:   1,  10,  50,  51;

Mathematica

cuaternas={}; Do[cuaternas=Join[cuaternas, {1, 2n, 2n^2, 2n^2+1}], {n, 1, 35}]; cuaternas

Crossrefs

Sequence in context: A371907 A368400 A325099 * A088177 A335917 A028507

Adjacent sequences: A370774 A370775 A370776 * A370778 A370779 A370780

Keyword

nonn,easy,tabf

Author

Miguel-Ángel Pérez García-Ortega, Mar 01 2024

Status

approved