A019309 Number of "bifix-free" words of length n over a four-letter alphabet.
1, 4, 12, 48, 180, 720, 2832, 11328, 45132, 180528, 721392, 2885568, 11539440, 46157760, 184619712, 738478848, 2953870260, 11815481040, 47261743632, 189046974528, 756187176720, 3024748706880, 12098991941952
Offset: 0
Links
- E. Barcucci, A. Bernini, S. Bilotta, R. Pinzani, Cross-bifix-free sets in two dimensions, arXiv preprint arXiv:1502.05275 [cs.DM], 2015.
- S. Bilotta, E. Pergola and R. Pinzani, A new approach to cross-bifix-free sets, arXiv preprint arXiv:1112.3168 [cs.FL], 2011.
- T. Harju and D. Nowotka, Border correlation of binary words.
- P. Tolstrup Nielsen, A note on bifix-free sequences, IEEE Trans. Info. Theory IT-19 (1973), 704-706.
Programs
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Mathematica
a[0]=1; a[n_]:=a[n]=4*a[n-1]-If[EvenQ[n], a[n/2], 0] (* Ed Pegg Jr, Jan 05 2005 *)
Formula
a(2n+1) = 4a(2n); a(2n) = 4a(2n-1) - a(n).