One of my friend asked me for help with this floorly sequence, but I also can't figured out for the solution what he wants. There is the sequence formed with four floor function which looks very unusual. I asked him for the sequence's meaning but he'll divulge it later when I found the solution. Without more preamble, he asked me to reform below two variable sequence to one variable sequence and also listed by value's size. $\phi _{k,n}=8+3\left \lfloor \frac{n}{2} \right \rfloor+7\left \lfloor \frac{n-1}{2} \right \rfloor+(2n+1)\left \lfloor \frac{k}{2} \right \rfloor+\left \{ 4n+2-(-1)^n \right \}\left \lfloor \frac{k-1}{2} \right \rfloor$ some values of the sequence are
$\phi _{k,1}=\left \{ 8, 11, 18, 21, 28, 31, \cdots \right \}$
$\phi _{k,2}=\left \{ 11, 16, 25, 30, 39, 44, \cdots \right \}$
$\phi _{k,3}=\left \{ 18, 25, 40, 47, 62, 69, \cdots \right \}$
$\phi _{k,4}=\left \{ 21, 30, 47, 56, 73, 82, \cdots \right \}$
$\phi _{k,5}=\left \{ 28, 39, 62, 73, 96, 107, \cdots \right \}$
$\phi _{k,6}=\left \{ 31, 44, 69, 82, 107, 120, \cdots \right \}$
and reformed sequence's values should be
$\Phi _{n}=\left \{ 8, 11, 16, 18, 21, 25, 28, 30, 31, \cdots \right \}$
On $\phi _{k,n}$, I tried to find the pattern of $k,n$ which correspondence with $\Phi _{n}$'s value, but I can't figured out it and I doubt there is general term of $k,n$ for my idea. More precisely, let $\alpha_m$ be the sequence of $\phi _{k,n}$'s $k$, and $\beta_m$ be the sequence of $\phi _{k,n}$'s $n$ which correspondence with $\Phi_n$'s value. If there is the general term of $\alpha_m$ and $\beta_m$, $\Phi_{m}$'s general term will be the formula below. $\Phi_{m}=8+3\left \lfloor \frac{\beta_m}{2} \right \rfloor+7\left \lfloor \frac{\beta_m-1}{2} \right \rfloor+(2\beta_m+1)\left \lfloor \frac{\alpha_m}{2} \right \rfloor+\left \{ 4\beta_m+2-(-1)^{\beta_{m}} \right \}\left \lfloor \frac{\alpha_m-1}{2} \right \rfloor$ But as you know, I can't get the general term of $\alpha_m$ and $\beta_m$. I need your help..also the solution.. Any new Idea and hint will be appreciated.