A395633 a(n) = number of triples (x, y, z) such that 2*x^2 + y*z = n, where x, y, z are positive integers satisfying y < x < z.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 3, 4, 3, 4, 3, 5, 3, 5, 3, 5, 4, 5, 3, 6, 3, 5, 4, 5, 3, 7, 4, 6, 5, 6, 4, 8, 4, 7, 5, 7, 4, 9, 4, 7, 6, 7, 4, 10, 4, 7, 6, 8, 5, 10, 5, 9, 7, 8, 5, 12, 5, 9, 7, 10, 5, 11, 6, 10

Offset

11,12

Links

Table of n, a(n) for n=11..94.

Example

a(28) = 3 counts these triples: (2, 1, 20), (3, 1, 10), (3, 2, 5).

Mathematica

t[n_, c_] := Module[{r}, r = Flatten[Table[If[n - 2 x^2 <= 0, {},
Map[({x, #, Quotient[n - 2 x^2, #]} &),
Select[Divisors[n - 2 x^2], Divisible[n - 2 x^2, #] &]]],
{x, 1, Floor[Sqrt[n - 1]]}], 1]; Select[r, Apply[c, #] &]];
c = (#2 < #1 < #3 &);
Table[Length[t[n, c]], {n, 11, 130}]
(* Peter J. C. Moses, Mar 29 2026 *)

Crossrefs

Cf. A393710, A394038, A394788, A395632.

Sequence in context: A217403 A378671 A081309 * A329377 A380783 A010553

Adjacent sequences: A395630 A395631 A395632 * A395634 A395635 A395636

Keyword

nonn

Author

Clark Kimberling, May 02 2026

Status

approved