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{\bf Mike Develin}
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{\bf A Complete Categorization of When Generalized \hfil\break
Tribonacci Sequences Can Be Avoided by \hfil\break
 Additive Partitions}
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A set or sequence $U$ in the natural numbers is defined to be
avoidable if
${\bf N}$ can be partitioned into two sets $A$ and $B$ such that no element of
$U$ is the sum of two distinct elements of $A$ or of two distinct elements
of $B$. In 1980, Hoggatt [5] studied the Tribonacci sequence
$T=\{t_n\}$ where $t_1=1$, $t_2=1$, $t_3=2$, and
$t_n=t_{n-1}+t_{n-2}+t_{n-3}$ for $n\ge 4$, and showed that it was
avoidable. Dumitriu [3] continued this research, investigating
Tribonacci sequences with arbitrary initial terms, and achieving partial
results. In this paper we give a complete answer to the question of
when a generalized Tribonacci sequence is avoidable.

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