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Algebra with sequences related to sqrt n

Source: Romanian TST 1979 day 2 P2

April 15, 2023
Sequencealgebra

Problem Statement

For each n∈Z>0n\in \mathbb{Z}_{>0} let ana_n be the closest integer to n\sqrt{n}. Compute the general term of the sequence: (bn)n⩾1(b_n)_{n\geqslant 1} with bn=∑k=1n2ak.b_n=\sum_{k=1}^{n^2} a_k.
Pall Dalyay
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