A331671 Number of Pythagorean triangles with sum of legs n.

0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 2, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 2, 0, 0, 0, 1

Offset

1,49

Links

Ray Chandler, Table of n, a(n) for n = 1..10000

Formula

a(n) = Sum_{k=1..floor((n-1)/2)} c(sqrt((n-k)^2+k^2)), where c(n) = 1-ceiling(n)+floor(n). - Wesley Ivan Hurt, Jun 26 2026

Mathematica

Table[Sum[1 - Ceiling[Sqrt[(n - k)^2 + k^2]] + Floor[Sqrt[(n - k)^2 + k^2]], {k, Floor[(n - 1)/2]}], {n, 100}] (* Wesley Ivan Hurt, Jun 26 2026 *)

Crossrefs

Cf. A118905, A198390, A254064.

Sequence in context: A113048 A392705 A394092 * A373925 A123758 A231642

Adjacent sequences: A331668 A331669 A331670 * A331672 A331673 A331674

Keyword

nonn,easy,changed

Author

Ray Chandler, Feb 26 2020

Status

approved