A395634 a(n) = number of triples (x, y, z) such that 2*x^2 + y*z = n, where x, y, z are positive integers with x coprime to y*z.

0, 0, 0, 1, 2, 2, 3, 2, 4, 3, 4, 5, 4, 4, 6, 4, 4, 7, 5, 5, 8, 4, 9, 10, 4, 6, 12, 5, 8, 10, 6, 6, 12, 6, 11, 12, 4, 10, 15, 6, 8, 13, 8, 11, 12, 6, 12, 16, 4, 8, 16, 8, 12, 20, 9, 8, 16, 12, 20, 17, 4, 10, 24, 10, 12, 16, 12, 15, 20, 8, 12, 20, 12, 15, 28

Offset

0,5

Links

Table of n, a(n) for n=0..74.

Example

a(11) = 5 counts these triples: (1,1,9), (1,3,3), (1,9,1), (2,1,3), (2,3,1).

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 = CoprimeQ[#1, #2 #3] &;
Join[{0}, Table[Length[t[n, c]], {n, 1, 130}]]
(* Peter J. C. Moses, Mar 29 2026 *)

Crossrefs

Cf. A393710, A394038, A394788, A395635.

Sequence in context: A162897 A364236 A356276 * A286532 A286622 A286589

Adjacent sequences: A395631 A395632 A395633 * A395635 A395636 A395637

Keyword

nonn

Author

Clark Kimberling, May 05 2026

Status

approved