I am trying to write a sequence ($a_n$) to denote number of matches at the $n$th figure.
I wrote first few terms: $a_1=3\;,a_2=5\;,a_3=7\;,a_4=9\;,a_5=11\;,\color\red{a_6=12}\quad$ therefore : $a_n=2n+1$ for $1\le n\le5$ continue this process: $a_7=14\;,a_8=16\;,a_9=18,\;\color\red{a_{10=}19}$. so $a_n=2n$ for $7\le n\le9$.
I realized the pattern: the difference between two consecutive term is $2$ but for $a_{4n+2}$ the difference is $1$. however I don't know how to write general term of sequence for this pattern.