MathDB
Combinatorial problem

Source: Moldova TST 2018

March 9, 2018
algorithmarithmetic sequencecombinatorics

Problem Statement

A pupil is writing on a board positive integers x0,x1,x2,x3...x_0,x_1,x_2,x_3... after the following algorithm which implies arithmetic progression 3,5,7,9...3,5,7,9....Each term of rank k≥2k\ge2 is a difference between the product of the last number on the board and the term of arithmetic progression of rank kk and the last but one term on the bord with the sum of the terms of the arithemtic progression with ranks less than kk.If x0=0x_0=0 and x1=1x_1=1 find xnx_n according to n.
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