Return to Answer

#Japt, 42 37 33 bytes

Japt is a shortened version of JavaScript. Interpreter

V=Un oU+1;Vr@X+(Vf_p2 +Y*Y¥U)l ,0

###How it works

           // Implicit: U = input number
V=Un oU+1  // Set variable V to range(-U, U+1). Ends up like [-U,-U+1,...,U-1,U]
Vr@    ,0  // Reduce each item Y in V with this function, starting at 0:
X+(     l  //  Return the previous value X + the length of:
Vf_p2      //   V filtered by items Z where Z*Z
+Y*Y==U)   //    + Y*Y equals U.
           // This ends up as the combined length of all fitting pairs of squares.
           // Implicit: return last expression

Perhaps there's a better technique; suggestions are welcome.

#Japt, 42 37 33 bytes

Japt is a shortened version of JavaScript. Interpreter

V=Un oU+1;Vr@X+(Vf_p2 +Y*Y¥U)l ,0

###How it works

           // Implicit: U = input number
V=Un oU+1  // Set variable V to range(-U, U+1). Ends up like [-U,-U+1,...,U-1,U]
Vr@    ,0  // Reduce each item Y in V with this function, starting at 0:
X+(     l  //  Return the previous value X + the length of:
Vf_p2      //   V filtered by items Z where Z*Z
+Y*Y==U)   //    + Y*Y equals U.
           // This ends up as the combined length of all fitting pairs of squares.
           // Implicit: return last expression

Perhaps there's a better technique; suggestions are welcome.

#Japt, 42 37 33 bytes

Japt is a shortened version of JavaScript. Interpreter

V=Un oU+1;Vr@X+(Vf_p2 +Y*Y¥U)l ,0

Explanation coming soon. Perhaps there's a better technique; suggestions are welcome.

#Japt, 42 37 33 bytes

Japt is a shortened version of JavaScript. Interpreter

V=Un oU+1;Vr@X+(Vf_p2 +Y*Y¥U)l ,0

###How it works

           // Implicit: U = input number
V=Un oU+1  // Set variable V to range(-U, U+1). Ends up like [-U,-U+1,...,U-1,U]
Vr@    ,0  // Reduce each item Y in V with this function, starting at 0:
X+(     l  //  Return the previous value X + the length of:
Vf_p2      //   V filtered by items Z where Z*Z
+Y*Y==U)   //    + Y*Y equals U.
           // This ends up as the combined length of all fitting pairs of squares.
           // Implicit: return last expression

Perhaps there's a better technique; suggestions are welcome.

#Japt, 42 37 bytes

Japt is a shortened version of JavaScript. Interpreter

Un oU+1 r@X+(Un oU+1 f_p2 +Y*Y¥U)l ,0

Explanation coming soon. Perhaps there's a better technique; suggestions are welcome.

#Japt, 42 37 33 bytes

Japt is a shortened version of JavaScript. Interpreter

V=Un oU+1;Vr@X+(Vf_p2 +Y*Y¥U)l ,0

Explanation coming soon. Perhaps there's a better technique; suggestions are welcome.