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A181787 Number of solutions to n^2 = a^2 + b^2 + c^2 with positive a, b, c. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 19 12:09 EDT 2021. Contains 345128 sequences. (Running on oeis4.)