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Putnam 2007 B3

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December 3, 2007
Putnamfloor functionlogarithmscalculusintegrationfunctioninduction

Problem Statement

Let x_0 \equal{} 1 and for n≥0, n\ge0, let x_{n \plus{} 1} \equal{} 3x_n \plus{} \left\lfloor x_n\sqrt {5}\right\rfloor. In particular, x_1 \equal{} 5,\ x_2 \equal{} 26,\ x_3 \equal{} 136,\ x_4 \equal{} 712. Find a closed-form expression for x2007. x_{2007}. (⌊a⌋ \lfloor a\rfloor means the largest integer ≤a. \le a.)
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