A097266 Number of primitive Pythagorean quadruples with diagonal 2n+1.

0, 1, 0, 1, 2, 2, 1, 2, 2, 3, 4, 3, 2, 5, 3, 4, 7, 4, 4, 6, 5, 6, 6, 6, 7, 9, 6, 6, 11, 8, 7, 12, 5, 9, 12, 9, 9, 10, 12, 10, 14, 11, 7, 14, 11, 12, 16, 10, 12, 19, 12, 13, 16, 14, 13, 18, 14, 12, 18, 16, 17, 21, 12, 16, 23, 17, 20, 18, 17, 18, 24, 18, 13, 28, 18, 19, 25, 16, 19, 26, 24

Offset: 0

Author

Ray Chandler, Aug 16 2004

Keywords

• nonn

Comments

There are no such quadruples with diagonal 2n. - Michael Somos, Nov 17 2018

Links

• Eric Weisstein's World of Mathematics, Pythagorean Quadruple.

Crossrefs

Cf. A096907-A096909, A097263-A097265.

Programs

Mathematica

a[ n_] := With[ {w = 2 n + 1}, Sum[ Boole[x^2 + y^2 + z^2 == w^2 && 1 == GCD[x, y, z, w]], {z, w - 1}, {y, z}, {x, y}]]; (* Michael Somos, Nov 17 2018 *)

PARI

{a(n) = my(w = 2*n+1); sum(z=1, w-1, sum(y=1, z, sum(x=1, y,  x^2 + y^2 + z^2 == w^2 && 1 == gcd([x, y, z, w]))))}; /* Michael Somos, Nov 17 2018 */