A complete categorization of when generalized Tribonacci sequences can be avoided by additive partitions
The electronic journal of combinatorics, Tome 7 (2000)
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.
@article{10_37236_1531,
author = {Mike Develin},
title = {A complete categorization of when generalized {Tribonacci} sequences can be avoided by additive partitions},
journal = {The electronic journal of combinatorics},
year = {2000},
volume = {7},
doi = {10.37236/1531},
zbl = {0964.05008},
url = {http://geodesic.mathdoc.fr/articles/10.37236/1531/}
}
Mike Develin. A complete categorization of when generalized Tribonacci sequences can be avoided by additive partitions. The electronic journal of combinatorics, Tome 7 (2000). doi: 10.37236/1531
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