No Two Consecutive Number

<?php
$t=0;
for($a=1;$a<=21;$a++){
for($b=$a+2;$b<=23;$b++){
for($c=$b+2;$c<=25;$c++){
$t++;
}
}
}
echo $t;
?>

Some quick and dirty loops gave me the correct answer, basically my theory was $a will always be the lowest number, $b will be the middle number and must be at least 2 greater than $a, and $c will be the highest number and must be 2 greater than $b.
$t just acts as a total and when we print it at the end it gives us our answer 1771

We look at the problem as a biner with the length of $25$ . $a_1a_2a_3\cdots a_{25}$ With $a_i$ is either $1$ or $0$ and we denote ( $1=a_i$ choosen) or ( $0=a_i$ not choosen) So We will put these $22$ number $0$ first, then we will choose the position of number $1$ between these $0$ so that there’s no two consecutive number will be selected. $+0+0+0+\cdots+0+0+0+$ The answer is $C^{23}_3=1771$