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。