smc

In the non-decreasing sequence of odd integers $\{a_1,a_2,a_3,\dots \}=\{1,3,3,3,5,5,5,5,5,\dots \}$ each odd positive integer $k$ appears $k$ times. It is a fact that there are integers $b,c$, and $d$ such that for all positive integers $n$, $a_n=b\lfloor \sqrt{n+c}\rfloor +d$, where $\lfloor x\rfloor$ denotes the largest integer not exceeding $x$. The sum $b+c+d$ equals