Voozh

A393713

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

0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 2, 3, 2, 4, 3, 4, 3, 4, 4, 4, 4, 4, 4, 6, 5, 5, 6, 5, 5, 7, 5, 6, 6, 6, 5, 9, 6, 7, 8, 7, 6, 10, 7, 7, 9, 8, 7, 9, 7, 10, 10, 8, 9, 11, 8, 9, 11, 10, 9, 11, 9, 11, 10, 10, 10, 14, 9, 11, 14, 11, 10, 13

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OFFSET

0,14

LINKS

Table of n, a(n) for n=0..79.

EXAMPLE

a(17) = 3 counts these triples: (2, 1, 13), (3, 1, 8), (3, 2, 4).

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, #] &]];