Recurring Styles #7 - Perfect Squares!

Probability Level 4

y n + 2 = ( 4 k − 5 ) y n + 1 − y n + 4 − 2 k , n ≥ 1 \large{y_{n+2} = (4k-5)y_{n+1} - y_n + 4 - 2k \ , \quad n \geq 1}

Define the sequence ( y n ) n = 1 ∞ (y_n)_{n=1}^\infty above by y 1 = y 2 = 1 y_1 = y_2 = 1 . Find the sum of all integers k k such that every term of the sequence is a perfect square.


The answer is 4.

Satyajit Mohanty by Satyajit Mohanty , 24, India

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