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Permutations of Project

Problem 458

Published on Sunday, 9th February 2014, 07:00 am; Solved by 375; 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".


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