<image>Embroidery from certain ethnic minorities has a long history. The images $$ (1) $$, $$ (2) $$, $$ (3) $$, and $$ (4) $$ below show their simplest embroidery patterns. These patterns are all composed of small squares. The more small squares there are, the more beautiful the embroidery appears. According to the same rule of embroidery (the same arrangement of small squares), let the nth pattern contain $$ f(n) $$ small squares.  $$(1)$$ Find $$ f(5) $$. $$(2)$$ Use inductive reasoning to deduce the relationship between $$ f(n{+}1) $$ and $$ f(n) $$. $$(3)$$ Based on the relationship you obtained, find the expression for $$ f(n) $$.