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A065458 Number of inequivalent (ordered) solutions to a^2 + b^2 + c^2 + d^2 = n^2.

%I A065458 #14 Feb 17 2015 08:25:43
%S A065458 1,1,2,2,2,3,4,4,2,6,7,6,4,8,10,14,2,11,14,13,7,23,15,17,4,24,21,31,
%T A065458 10,25,37,28,2,46,29,49,14,38,35,61,7,45,62,49,15,93,47,57,4,72,67,97,
%U A065458 21,71,84,101,10,119,70,86,37,92,79,165,2,138,127,109,29,168,140,121,14
%N A065458 Number of inequivalent (ordered) solutions to a^2 + b^2 + c^2 + d^2 = n^2.
%H A065458 Alois P. Heinz, <a href="/A065458/b065458.txt">Table of n, a(n) for n = 0..1000</a>
%e A065458 a(5)=3 because 25 produces {0,0,0,5}, {0,0,3,4}, {1,2,2,4}.
%p A065458 N:= 100:
%p A065458 R:= Vector(N,1):
%p A065458 for a from 0 to N do
%p A065458   for b from a to floor(sqrt(N^2-a^2)) do
%p A065458      for c from b to floor(sqrt(N^2-a^2-b^2)) do
%p A065458        q:= a^2 + b^2 + c^2;
%p A065458        for f in numtheory:-divisors(q) do
%p A065458           if f^2 + 2*f*c <= q and (f + q/f)::even then
%p A065458              r:= (f + q/f)/2;
%p A065458              if r <= N then R[r]:= R[r]+1 fi;
%p A065458           fi
%p A065458 od od od od:
%p A065458 convert(R,list); # _Robert Israel_, Feb 16 2015
%t A065458 Length/@Table[SumOfSquaresRepresentations[4, (k)^2], {k, 72}]
%Y A065458 Cf. A063014, A016727, A065459.
%Y A065458 Column k=4 of A255212.
%K A065458 nonn
%O A065458 0,3
%A A065458 _Wouter Meeussen_, Nov 18 2001
%E A065458 a(0)=1 prepended by _Alois P. Heinz_, Feb 17 2015