A181787 Number of solutions to n^2 = a^2 + b^2 + c^2 with positive a, b, c.

0, 0, 0, 3, 0, 0, 3, 6, 0, 12, 0, 9, 3, 6, 6, 15, 0, 9, 12, 15, 0, 33, 9, 18, 3, 12, 6, 39, 6, 18, 15, 24, 0, 48, 9, 30, 12, 24, 15, 45, 0, 27, 33, 33, 9, 60, 18, 36, 3, 48, 12, 60, 6, 36, 39, 45, 6, 78, 18, 45, 15, 42, 24, 114, 0, 36, 48, 51, 9, 93, 30, 54, 12, 51, 24, 87, 15, 87, 45, 60, 0, 120, 27, 63, 33, 51, 33, 105, 9, 63, 60, 84, 18, 123, 36, 75, 3, 69, 48, 165, 12

Offset

0,4

Comments

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

Links

Robert Israel, Table of n, a(n) for n = 0..2000

Formula

a(n) = A063691(n^2). - Michel Marcus, Apr 25 2015

a(2*n) = a(n). - Robert Israel, Aug 02 2019

Example

a(3)=3 because 3^2 = 1^2+2^2+2^2 = 2^2+1^2+2^2 = 2^2+2^2+1^2. - Robert Israel, Aug 02 2019

Maple

N:= 200: # for a(0)..a(N)
A:= Array(0..N):
mults:= [1, 3, 6]:
for a from 1 while 3*a^2 <= N^2 do
  if a::odd then b0:= a+1; db:= 2 else b0:= a; db:= 1 fi;
  for b from b0 by db while a^2 + 2*b^2 <= N^2 do
    if (a+b)::odd then c0:= b + (b mod 2); dc:= 2 else c0:= b; dc:= 1 fi;
    for c from c0 by dc do
      v:= a^2 + b^2 + c^2;
      if v > N^2 then break fi;
      if issqr(v) then
        w:= sqrt(v);
        A[w]:= A[w]+ mults[nops({a, b, c})];
      fi
od od od:
convert(A, list); # Robert Israel, Aug 02 2019

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, nn}, {c, nn}]; Prepend[t, 0]

Crossrefs

Cf. A016725, A016727, A181786, A181788.

Sequence in context: A037285 A337981 A341761 * A318925 A285213 A285339

Adjacent sequences: A181784 A181785 A181786 * A181788 A181789 A181790

Keyword

nonn,look

Author

T. D. Noe, Nov 12 2010

Status

approved