1980 AMC 12 Problema 25

In the nondecreasing sequence of odd integers $$\begin{aligned} (a_1,a_2,a_3,\ldots) ={}&(1,3,3,3,\\ &5,5,5,5,5,\ldots) \end{aligned}$$ each positive odd integer $k$ appears $k$ times. It is a fact that there are integers $b,$ $c,$ and $d$ such that, for all positive integers $n,$ $$a_n=b\left\lfloor\sqrt{n+c}\right\rfloor+d,$$ where $\lfloor x\rfloor$ denotes the largest integer not exceeding $x.$ The sum $b+c+d$ equals