MathDB
2020 PUMaC Team 12

Source:

January 1, 2022
algebra

Problem Statement

Given a sequence a0,a1,a2,...,ana_0, a_1, a_2, ... , a_n, let its arithmetic approximant be the arithmetic sequence b0,b1,...,bnb_0, b_1, ... , b_n that minimizes the quantity ∑i=0n(bi−ai)2\sum_{i=0}^{n}(b_i -a_i)^2, and denote this quantity the sequence’s anti-arithmeticity. Denote the number of integer sequences whose arithmetic approximant is the sequence 44, 88, 1212, 1616 and whose anti-arithmeticity is at most 2020.
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