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Problem 458


Problem 458


Permutations of Project

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.


Project的重排

考虑单词“Project”中的字母构成的字符集A={c,e,j,o,p,r,t}。
记T(n)是由A中的字符构成的长度为n且不包含有“project”的5040种重排中任何一个为其子串的字符串数目。

已知T(7)=77-7!=818503。

求T(1012),并给出其最后9位数字。