A082659 Integers expressible as the sum of a square and a triangular number in exactly three distinct ways.

10, 19, 46, 64, 82, 109, 121, 127, 154, 169, 217, 253, 257, 262, 271, 316, 352, 361, 379, 397, 400, 451, 460, 478, 487, 496, 505, 514, 529, 586, 620, 640, 649, 667, 694, 721, 757, 767, 856, 865, 910, 937, 961, 964, 991, 1045, 1054, 1072, 1099, 1104, 1135, 1153

Offset: 1

Author

Jason Earls, May 17 2003

Keywords

• nonn

Comments

It is assumed here that 0 is a square but not a triangular number. - Amiram Eldar, Dec 08 2019

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

Mathematica

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 *)

Extensions

Name clarified by Amiram Eldar, Dec 08 2019