Mathegoras

Sequences and series › Recursive sequences › Computing terms of a recurrence

Sequence with a quadratic shift relation

High school · ●●●○○ 50 pts

Let the sequence a0,a1,a2,…a_0, a_1, a_2, \ldots satisfy a0=a1=11a_0=a_1=11 and am+n=12(a2m+a2n)−(m−n)2a_{m+n}=\frac{1}{2}\left(a_{2m}+a_{2n}\right)-(m-n)^2 for all integers m,n⩾0m, n \geqslant 0. Find a45a_{45}.

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sequencesquadratic sequences