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%I #33 Sep 16 2016 12:58:11
%S 1,3,6,18,48,144,414,1242,3678,11034,32958,98874,296208,888624,
%T 2664630,7993890,23977992,71933976,215790894,647372682,1942085088,
%U 5826255264,17478666918,52436000754,157307706054,471923118162
%N Number of "bifix-free" words of length n over a three-letter alphabet.
%H E. Barcucci, A. Bernini, S. Bilotta, R. Pinzani, <a href="http://arxiv.org/abs/1502.05275">Cross-bifix-free sets in two dimensions</a>, arXiv preprint arXiv:1502.05275 [cs.DM], 2015.
%H S. Bilotta, E. Pergola and R. Pinzani, <a href="http://arxiv.org/abs/1112.3168">A new approach to cross-bifix-free sets</a>, arXiv preprint arXiv:1112.3168 [cs.FL], 2011.
%H Joshua Cooper and Danny Rorabaugh, <a href="http://arxiv.org/abs/1510.03917">Asymptotic Density of Zimin Words</a>, arXiv preprint arXiv:1510.03917
%H T. Harju and D. Nowotka, <a href="http://www.tucs.fi/Publications/attachment.php?fname=TR546.pdf">Border correlation of binary words</a>.
%H P. Tolstrup Nielsen, <a href="http://dx.doi.org/10.1109/TIT.1973.1055065">A note on bifix-free sequences</a>, IEEE Trans. Info. Theory IT-19 (1973), 704-706.
%H D Rorabaugh, <a href="http://arxiv.org/abs/1509.04372">Toward the Combinatorial Limit Theory of Free Words</a>, arXiv preprint arXiv:1509.04372, 2015
%F a(2n+1) = 3a(2n); a(2n) = 3a(2n-1) - a(n).
%t a[0]=1; a[n_]:=a[n]=3*a[n-1]-If[EvenQ[n], a[n/2], 0] (* _Ed Pegg Jr_, Jan 05 2005 *)
%Y Equals 3*A045694(n) for n>0. Cf. A003000, A019309.
%K nonn
%O 0,2
%A _Jeffrey Shallit_
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