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%I #25 Dec 01 2015 09:00:54
%S 1,4,12,48,180,720,2832,11328,45132,180528,721392,2885568,11539440,
%T 46157760,184619712,738478848,2953870260,11815481040,47261743632,
%U 189046974528,756187176720,3024748706880,12098991941952
%N Number of "bifix-free" words of length n over a four-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 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.
%F a(2n+1) = 4a(2n); a(2n) = 4a(2n-1) - a(n).
%t a[0]=1; a[n_]:=a[n]=4*a[n-1]-If[EvenQ[n], a[n/2], 0] (* _Ed Pegg Jr_, Jan 05 2005 *)
%Y Cf. A003000, A019308, A094547, A094559, A094578.
%K nonn,easy
%O 0,2
%A _Jeffrey Shallit_
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