OFFSET
1,1
COMMENTS
REFERENCES
T. Nagell, Introduction to Number Theory, Wiley, 1951, p. 194.
LINKS
Robert Israel, Table of n, a(n) for n = 1..3140
O. Fraser and B. Gordon, On representing a square as the sum of three squares, Amer. Math. Monthly, 76 (1969), 922-923.
EXAMPLE
9 = 1 + 4 + 4,
36 = 16 + 16 + 4,
49 = 36 + 9 + 4,
81 = 49 + 16 + 16,
so these are in the sequence.
16 cannot be written as the sum of 3 squares if zero is not allowed, therefore 16 is not in the sequence.
Also we can see that 49-36-9-4=0, so (7,6,3,2) is a null vector in the signatures (+,-,-,-) and (-,+,+,+). - Jon Perry, Oct 06 2012
MAPLE
M:= 10000: # to get all terms <= M
sort(convert(select(issqr, {seq(seq(seq(x^2 + y^2 + z^2,
z=y..floor(sqrt(M-x^2-y^2))), y=x..floor(sqrt((M-x^2)/2))),
x=1..floor(sqrt(M/3)))}), list)); # Robert Israel, Jan 28 2016
MATHEMATICA
Select[Range[60]^2, Resolve@ Exists[{x, y, z}, Reduce[# == x^2 + y^2 + z^2, {x, y, z}, Integers], And[x > 0, y > 0, z > 0]] &] (* Michael De Vlieger, Jan 27 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Mar 02 2010
STATUS
approved