Voozh

A393712

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

0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 3, 0, 1, 2, 2, 0, 3, 1, 2, 2, 1, 1, 5, 1, 1, 3, 4, 0, 4, 1, 3, 4, 1, 2, 6, 0, 3, 4, 5, 0, 4, 3, 4, 5, 1, 1, 8, 1, 4, 5, 4, 2, 4, 3, 5, 5, 3, 2, 9, 0, 2, 8, 6, 2, 6, 2, 6, 4, 4, 3, 9, 4, 2, 8, 3, 1, 9, 2, 10, 5, 1, 4, 10

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OFFSET

0,14

LINKS

Table of n, a(n) for n=0..85.

EXAMPLE

a(19) = 3 counts these triples: (1, 2, 9), (1, 3, 6), (2, 3, 5).

MATHEMATICA

t[n_, c_] := Module[{r}, r = Flatten[Table[If[n - x^2 <= 0, {},

Map[({x, #, Quotient[n - x^2, #]} &),

Select[Divisors[n - x^2], Divisible[n - x^2, #] &]]], {x, 1,

Floor[Sqrt[n - 1]]}], 1]; Select[r, Apply[c, #] &]];