A Familiar Recurrence Occurs Again

作者:Leonard I E*; Liu A C F
来源:American Mathematical Monthly, 2012, 119(4): 333-336.
DOI:10.4169/amer.math.monthly.119.04.333

摘要

An explicit solution is given to a familiar third order recurrence relation
a(n+3) = a(n+1) + a(n), n >= 0
a(0) = 3, a(1) = 0, a(3) = 2.
A proof using elementary number theory is given to show that a(n) is prime-divisible. That is, if n is prime, then n vertical bar a(n).

  • 出版日期2012-4

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