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Integers expressible as the sum of a square and a triangular number in exactly three distinct ways.
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%I #15 Dec 08 2019 12:25:18

%S 10,19,46,64,82,109,121,127,154,169,217,253,257,262,271,316,352,361,

%T 379,397,400,451,460,478,487,496,505,514,529,586,620,640,649,667,694,

%U 721,757,767,856,865,910,937,961,964,991,1045,1054,1072,1099,1104,1135,1153

%N Integers expressible as the sum of a square and a triangular number in exactly three distinct ways.

%C It is assumed here that 0 is a square but not a triangular number. - _Amiram Eldar_, Dec 08 2019

%H Amiram Eldar, <a href="/A082659/b082659.txt">Table of n, a(n) for n = 1..10000</a>

%e a(5) = 82 because 82 = 1 + 81; 82 = 66 + 16; 82 = 78 + 4.

%t aQ[n_] := Length @ Solve[x^2 + y (y + 1)/2 == n && x >= 0 && y > 0, {x, y}, Integers] == 3; Select[Range[1200], aQ] (* _Amiram Eldar_, Dec 08 2019 *)

%Y Cf. A000217, A000290, A082657, A082658, A082660.

%K nonn

%O 1,1

%A _Jason Earls_, May 17 2003

%E Name clarified by _Amiram Eldar_, Dec 08 2019