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 August 18th, 2013, 04:27 PM #1 Newbie   Joined: Aug 2013 Posts: 3 Thanks: 0 Recurrence Relation of a Sequence The problem is at: http://sdrv.ms/13KJBit Can anyone figure it out? I've made a start, but not producing anything fruitful so far, answer is an integer from 0 to 999.
 August 18th, 2013, 05:54 PM #2 Global Moderator   Joined: Dec 2006 Posts: 18,034 Thanks: 1393 The sequence $x_{\small0},\,x_{\small1},\,x_{\small2},\,.\,.\,.$ is defined by the recurrence relation       $x_{n\small+1}\,=\,ax_n\,+\,bx_{n\small-1}\,+\,cx_{n\small-2}\,+\,dx_{n\small-3},\,n\,\ge\,3.$ For fixed integers $^{a,\,b,\,c,\,d,}$ it turns out that regardless of the initial values $x_{\small0},\,x_{\small1},\,x_{\small2},\,x_{\smal l3},$ the sequence is eventually periodic. Find the sum of all possible periods.

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