Eventual universality for four signed pentagonal forms

Let $\mathbb N$ denote the nonnegative integers and define

$$N(1)=114862,\qquad N(-1)=166897,\qquad N(3)=196987,\qquad N(-3)=273118.$$

Signed pentagonal universality conjecture. For each $r\in\{\pm1,\pm3\}$, every integer $n>N(r)$ can be written as

$$n=\frac{x(5x+r)}2+\frac{y(5y+r)}2+\frac{z(5z+r)}2$$

with $x,y,z\in\mathbb N$.

The conjecture gives explicit bounds for eventual universality for four ternary sums, one for each allowed linear coefficient $r$. No resolution is given in the source.