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x_0 = 0, x_{k+1} = [(n - \sum_0^k x_i)/2

Source: 1991 Swedish Mathematical Competition p3

April 2, 2021
Sequencealgebra

Problem Statement

The sequence x0,x1,x2,...x_0, x_1, x_2, ... is defined by x0=0x_0 = 0, xk+1=[(n−∑0kxi)/2]x_{k+1} = [(n - \sum_0^k x_i)/2]. Show that xk=0x_k = 0 for all sufficiently large kk and that the sum of the non-zero terms xkx_k is n−1n-1.
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