Permutations of Project (noch nicht übersetzt)

Consider the alphabet A made out of the letters of the word "project": A={c,e,j,o,p,r,t}.
Let T(n) be the number of strings of length n consisting of letters from A that do not have a substring that is one of the 5040 permutations of "project".

T(7)=7⁷-7!=818503.

Find T(10¹²). Give the last 9 digits of your answer.