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n-sequences

Problem 427

Published on 11 May 2013 at 10:00 pm [Server Time]

A sequence of integers S = {si} is called an n-sequence if it has n elements and each element si satisfies 1 ≤ si ≤ n. Thus there are nn distinct n-sequences in total. For example, the sequence S = {1, 5, 5, 10, 7, 7, 7, 2, 3, 7} is a 10-sequence.

For any sequence S, let L(S) be the length of the longest contiguous subsequence of S with the same value. For example, for the given sequence S above, L(S) = 3, because of the three consecutive 7's.

Let f(n) = ∑ L(S) for all n-sequences S.

For example, f(3) = 45, f(7) = 1403689 and f(11) = 481496895121.

Find f(7 500 000) mod 1 000 000 009.


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