Binomial Coefficients in Piecewise Function

Question

is there a way to get binomial coefficients to appear inside a piecewise function? This is the code I am using right now:

$$ a(n,3)=% 

   \begin{cases}

     $ 1 {{k+2}\choose{2}} + 4 {{k+1}\choose{2}} + 1 {{k}\choose{2}}$ &\text{if $n\equiv0$ $\mod d$} \\
     $ 1 {{k+2}\choose{2}} + 5 {{k+1}\choose{2}} $ &\text{if $n\equiv1$ $\mod d$} \\
     $ 2 {{k+2}\choose{2}} + 4 {{k+1}\choose{2}} $ &\text{if $n\equiv d-1$ $\mod d$} \\
     $ 3 {{k+2}\choose{2}} + 3 {{k+1}\choose{2}} $ &\text{if $n\equiv d-1$ $\mod d$} \\
     $ 4 {{k+2}\choose{2}} + 2 {{k+1}\choose{2}} $ &\text{if $n\equiv d-1$ $\mod d$} \\
     $ 5 {{k+2}\choose{2}} + 1 {{k+1}\choose{2}} $ &\text{if $n\equiv d-1$ $\mod d$} \\
   \end{cases} $$

And This is the way that it is showing up.

I need it to say

$1({k+2}\choose{2}) + 4 ({k+1}\choose{2})$,

and so on. I've tried putting extra brackets, but it still won't fix the formatting.

Answer 1

Welcome! You should no longer use $$ nor \choose. Also you should not add unnecessary $ signs. Here I think the dcases from mathtools makes sense.

\documentclass{article}
\usepackage{mathtools}
\begin{document}
\[
a(n,3)=%
\begin{dcases}
  1 \binom{k+2}{2} + 4 \binom{k+1}{2} + 1 \binom{k}{2} &
    \text{if }n\equiv0 \mod d \\
  1 \binom{k+2}{2} + 5 \binom{k+1}{2}  &\text{if }n\equiv1 \mod d\\
  2 \binom{k+2}{2} + 4 \binom{k+1}{2}  &\text{if }n\equiv d-1 \mod d\\
  3 \binom{k+2}{2} + 3 \binom{k+1}{2}  &\text{if }n\equiv d-1 \mod d\\
  4 \binom{k+2}{2} + 2 \binom{k+1}{2}  &\text{if }n\equiv d-1 \mod d\\
  5 \binom{k+2}{2} + 1 \binom{k+1}{2}  &\text{if }n\equiv d-1 \mod d\\
\end{dcases} 
\]
\end{document}