A Branching Integer Recurrence
Difficulty: Hard · Topics: Algebra, Sequences, Recurrences
Tarmoqlanuvchi butun sonli rekurrent munosabat
The first term of \a n\ is an integer, and for every natural number n,
a n+1=begincasesa n-6, & a n≥ 0\\ -3a n+2, & a n<0.endcases
Over all such sequences with a 4+a 5=10, let M and m be the largest and smallest values of Σ k=1^103a k. Find M-m.
\a n\ ning birinchi hadi butun son va har bir natural n uchun
a n+1=begincasesa n-6, & a n≥ 0\\ -3a n+2, & a n<0.endcases
a 4+a 5=10 bo‘lgan barcha shunday ketma-ketliklar bo‘yicha Σ k=1^103a k ning eng katta va eng kichik qiymatlari M va m bo‘lsin. M-m ni toping.