A065458 - OEIS

%I #14 Feb 17 2015 08:25:43

%S 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 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 21,71,84,101,10,119,70,86,37,92,79,165,2,138,127,109,29,168,140,121,14

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

%H Alois P. Heinz, <a href="/A065458/b065458.txt">Table of n, a(n) for n = 0..1000</a>

%e a(5)=3 because 25 produces {0,0,0,5}, {0,0,3,4}, {1,2,2,4}.

%p N:= 100:

%p R:= Vector(N,1):

%p for a from 0 to N do

%p   for b from a to floor(sqrt(N^2-a^2)) do

%p      for c from b to floor(sqrt(N^2-a^2-b^2)) do

%p        q:= a^2 + b^2 + c^2;

%p        for f in numtheory:-divisors(q) do

%p           if f^2 + 2*f*c <= q and (f + q/f)::even then

%p              r:= (f + q/f)/2;

%p              if r <= N then R[r]:= R[r]+1 fi;

%p           fi

%p od od od od:

%p convert(R,list); # _Robert Israel_, Feb 16 2015

%t Length/@Table[SumOfSquaresRepresentations[4, (k)^2], {k, 72}]

%Y Cf. A063014, A016727, A065459.

%Y Column k=4 of A255212.

%K nonn

%O 0,3

%A _Wouter Meeussen_, Nov 18 2001

%E a(0)=1 prepended by _Alois P. Heinz_, Feb 17 2015