A181786 Number of inequivalent solutions to n^2 = a^2 + b^2 + c^2 with positive a, b, c.

0, 0, 0, 1, 0, 0, 1, 1, 0, 3, 0, 2, 1, 1, 1, 3, 0, 2, 3, 3, 0, 6, 2, 3, 1, 2, 1, 8, 1, 3, 3, 4, 0, 10, 2, 5, 3, 4, 3, 8, 0, 5, 6, 6, 2, 11, 3, 6, 1, 8, 2, 12, 1, 6, 8, 8, 1, 15, 3, 8, 3, 7, 4, 20, 0, 6, 10, 9, 2, 16, 5, 9, 3, 9, 4, 15, 3, 15, 8, 10, 0, 22, 5, 11, 6, 9, 6, 18, 2, 11, 11, 14, 3, 21, 6, 13, 1, 12, 8, 31, 2

Offset: 0

Author

T. D. Noe, Nov 12 2010

Keywords

• nonn

Comments

Note that a(n)=0 for n=0 and the n in A094958.

Also note that a(2n)=a(n), e.g., a(1000)=a(500)=a(250)=a(125)=14. - Zak Seidov, Mar 02 2012

a(n) is the number of distinct parallelepipeds each one having integer diagonal n and integer sides. - César Eliud Lozada, Oct 26 2014

Links

• Samuel Harkness, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Zak Seidov)

Crossrefs

Cf. A016725, A016727, A046080, A181787, A181788

Programs

Mathematica

nn=100; t=Table[0,{nn}]; Do[n=Sqrt[a^2+b^2+c^2]; If[n<=nn && IntegerQ[n], t[[n]]++], {a,nn}, {b,a,nn}, {c,b,nn}]; Prepend[t,0]