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URL: https://oeis.org/A375016

⇱ A375016 - OEIS

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A375016
Number of 1-unbordered words of length n over a 3-letter alphabet beginning with a fixed letter.
0
1, 1, 3, 7, 21, 57, 171, 499, 1497, 4449, 13347, 39927, 119781, 359001, 1077003, 3230011, 9690033, 29067105, 87201315, 261595047, 784785141, 2354328729, 7062986187, 21188878707, 63566636121, 190699668801, 572099006403, 1716296301207, 5148888903621, 15446664556857
OFFSET
1,3
COMMENTS
a(n) is equal to the number of short leaves in the tautological degree 3 lamination at depth n+1.
LINKS
Danny Calegari, Combinatorics of the Tautological Lamination, arXiv:2106.00578, [math.DS], 2021-2024.
Danny Calegari, Combinatorics of the Tautological Lamination, Pacific J. Math. 329 (2024) 39-61.
FORMULA
a(1) = 1; a(2*n+1) = 3*a(2*n) for n > 0; a(2*n) = 3*a(2*n-1) - 2*a(n) for n > 0.
PROG
(PARI) a(n) = if (n==1, 1, if (n%2, 3*a(n-1), 3*a(n-1)-2*a(n/2))); \\ Michel Marcus, Aug 09 2024
CROSSREFS
Sequence in context: A262184 A091489 A374721 * A104779 A178718 A244897
KEYWORD
nonn
AUTHOR
Danny Calegari, Aug 08 2024
EXTENSIONS
More terms from Michel Marcus, Aug 09 2024
STATUS
approved