%I #42 Aug 16 2024 21:18:03
%S 1,1,3,7,21,57,171,499,1497,4449,13347,39927,119781,359001,1077003,
%T 3230011,9690033,29067105,87201315,261595047,784785141,2354328729,
%U 7062986187,21188878707,63566636121,190699668801,572099006403,1716296301207,5148888903621,15446664556857
%N Number of 1-unbordered words of length n over a 3-letter alphabet beginning with a fixed letter.
%C a(n) is equal to the number of short leaves in the tautological degree 3 lamination at depth n+1.
%H Danny Calegari, <a href="https://arxiv.org/abs/2106.00578">Combinatorics of the Tautological Lamination</a>, arXiv:2106.00578, [math.DS], 2021-2024.
%H Danny Calegari, <a href="https://doi.org/10.2140/pjm.2024.329.39">Combinatorics of the Tautological Lamination</a>, Pacific J. Math. 329 (2024) 39-61.
%F 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.
%o (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
%K nonn
%O 1,3
%A _Danny Calegari_, Aug 08 2024
%E More terms from _Michel Marcus_, Aug 09 2024