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

1,1

Comments

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

Links

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A372096 A298487 A359315 * A088409 A219959 A307344

Adjacent sequences: A082656 A082657 A082658 * A082660 A082661 A082662

Keyword

nonn

Author

Jason Earls, May 17 2003

Extensions

Name clarified by Amiram Eldar, Dec 08 2019

Status

approved