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%I #9 Apr 22 2015 17:24:47
%S 45,48,63,64,72,75,80,81,99,112,117,128,147,153,171,175,176,180,200,
%T 207,208,243,245,252,261,272,275,279,300,304,324,325,333,363,368,369,
%U 387,392,396,423,425,464,468,475,477,496,507,531,539,549,575,588,592
%N Values of n such that there are exactly 3 solutions to x^2 - y^2 = n with x > y >= 0.
%H Colin Barker, <a href="/A257410/b257410.txt">Table of n, a(n) for n = 1..500</a>
%e 45 is in the sequence because there are 3 solutions to x^2 - y^2 = 45, namely (x,y) = (7,2),(9,6),(23,22).
%t r[n_] := Reduce[x^2 - y^2 == n && x > y >= 0, {x, y}, Integers]; Reap[For[n = 1, n < 600, n++, rn = r[n]; If[rn[[0]] === Or && Length[rn] == 3, Print[n]; Sow[n]]]][[2, 1]] (* _Jean-François Alcover_, Apr 22 2015 *)
%o (PARI) is_A257410(n)={A034178(n)==3} \\ _M. F. Hasler_, Apr 22 2015
%Y Cf. A257408, A257409, A257411-A257417.
%Y Cf. A034178.
%K nonn
%O 1,1
%A _Colin Barker_, Apr 22 2015
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