

A082659


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


4



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
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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: A245003 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



