## Permutations of Project

### Problem 458

Published on Sunday, 9th February 2014, 07:00 am; Solved by 422; Difficulty rating: 30%
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".

^{7}-7!=818503.

Find T(10^{12}). Give the last 9 digits of your answer.