A019308 Number of "bifix-free" words of length n over a three-letter alphabet.
1, 3, 6, 18, 48, 144, 414, 1242, 3678, 11034, 32958, 98874, 296208, 888624, 2664630, 7993890, 23977992, 71933976, 215790894, 647372682, 1942085088, 5826255264, 17478666918, 52436000754, 157307706054, 471923118162
Offset: 0
Keywords
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.
- Joshua Cooper and Danny Rorabaugh, Asymptotic Density of Zimin Words, arXiv preprint arXiv:1510.03917
- 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.
- D Rorabaugh, Toward the Combinatorial Limit Theory of Free Words, arXiv preprint arXiv:1509.04372, 2015
Programs
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Mathematica
a[0]=1; a[n_]:=a[n]=3*a[n-1]-If[EvenQ[n], a[n/2], 0] (* Ed Pegg Jr, Jan 05 2005 *)
Formula
a(2n+1) = 3a(2n); a(2n) = 3a(2n-1) - a(n).