Shell variables are allowed as operands; parameter expansion is performed before
the expression is evaluated. Within an expression, shell variables may also be
referenced by name without using the parameter expansion syntax.
Therefore explicit parameter expansion syntax (introduced by the $ character) is not necessary to reference the shell variable within the $((...)) (arithmetic expansion) on this line.
Quoting
man bash
, underARITHMETIC EVALUATION
:Therefore explicit parameter expansion syntax (introduced by the
$
character) is not necessary to reference the shell variable within the$((...))
(arithmetic expansion) on this line.