EPISODE · Jul 29, 2025 · 5 MIN
OEIS A000288: The all-ones tetranacci sequence
from Intellectually Curious · host Mike Breault
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.Note: This podcast was AI-generated, and sometimes AI can make mistakes. Please double-check any critical information.Sponsored by Embersilk LLC
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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...
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OEIS A000288: The all-ones tetranacci sequence
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