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A181786 Number of inequivalent solutions to n^2 = a^2 + b^2 + c^2 with positive a, b, c. 6


%S 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,

%T 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,

%U 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

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

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

%C Also note that a(2n)=a(n), e.g., a(1000)=a(500)=a(250)=a(125)=14. - _Zak Seidov_, Mar 02 2012

%C a(n) is the number of distinct parallelepipeds each one having integer diagonal n and integer sides. - _C├ęsar Eliud Lozada_, Oct 26 2014

%H Zak Seidov, <a href="/A181786/b181786.txt">Table of n, a(n) for n = 0..1000</a>

%t 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]

%Y Cf. A016725, A016727, A181787, A181788

%K nonn

%O 0,10

%A _T. D. Noe_, Nov 12 2010

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Last modified August 1 13:01 EDT 2021. Contains 346391 sequences. (Running on oeis4.)