OEIS A000288: The all-ones tetranacci sequence

We explore A000288, the tetranacci-type sequence with starting values 1,1,1,1. Its simple recurrence a(n)=a(n−1)+a(n−2)+a(n−3)+a(n−4) leads to surprising structure: a combinatorial interpretation counting 4-letter words over {0,1,2,3} with the rule that each 1, 2, or 3 must be followed by at least one, two, or three zeros respectively; it also exhibits Benford-like leading-digit distribution and grows with the tetranacci constant around 1.92756. We’ll also touch on its generating function and what these properties reveal about the richness lurking in simple recurrences.

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