Anti-Recurrence Sequences

We extend the work of Kimberling and Moses, Zaslavsky, and Bosma et al. on anti-recurrence sequences. Kimberling and Moses formulated several questions about these sequences, which together suggest the meta-conjecture that every antirecurrence sequence is the sum of a linear progression and an automatic sequence. We solve this conjecture under a restriction on the linear form that generates the anti-recurrence.