A375016 Number of 1-unbordered words of length n over a 3-letter alphabet beginning with a fixed letter.

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

Table of n, a(n) for n=1..30.

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

Adjacent sequences: A375013 A375014 A375015 * A375017 A375018 A375019

Keyword

nonn

Author

Danny Calegari, Aug 08 2024

Extensions

More terms from Michel Marcus, Aug 09 2024

Status

approved