MathDB
SMO 2008 q3

Source: SMO 2008, open, second round

March 30, 2018
Sequence

Problem Statement

let n,m be positive integers st m>n≥5m>n\geq 5 with m depending on n. consider the sequence a1,a2,...ama_1,a_2,...a_m where ai=ia_i=i for i=1,...,ni=1,...,n an+j=a3j+a3j−1+a3j−2a_{n+j}=a_{3j}+a_{3j-1}+a_{3j-2} for j=1,..,m−nj=1,..,m-n with m−3(m−n)=m-3(m-n)=1 or 2, ie am=am−k+am−k−1+am−k−2a_m=a_{m-k}+a_{m-k-1}+a_{m-k-2} where k=1 or 2 (Thus if n=5n=5, the sequence is 1,2,3,4,5,6,15 and if n=8n=8, the sequence is 1,2,3,4,5,6,7,8,6,15,21) Find S=a1+...+amS=a_1+...+a_m if (i) n=2007n=2007 (ii) n=2008n=2008
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