login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A019308 Number of "bifix-free" words of length n over a three-letter alphabet. 9
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..25.

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

FORMULA

a(2n+1) = 3a(2n); a(2n) = 3a(2n-1) - a(n).

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 *)

CROSSREFS

Equals 3*A045694(n) for n>0. Cf. A003000, A019309.

Sequence in context: A108507 A287212 A083337 * A000932 A187124 A161006

Adjacent sequences:  A019305 A019306 A019307 * A019309 A019310 A019311

KEYWORD

nonn

AUTHOR

Jeffrey Shallit

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 18 22:48 EDT 2020. Contains 337174 sequences. (Running on oeis4.)