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A019308
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Number of "bifix-free" words of length n over a three-letter alphabet.
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6
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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; internal format)
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OFFSET
| 0,2
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REFERENCES
| P. Tolstrup Nielsen, A note on bifix-free sequences, IEEE Trans. Inform. Theory IT-19 (1973), 704-706.
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LINKS
| T. Harju and D. Nowotka, Border correlation of binary words.
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FORMULA
| a(2n+1) = 3a(2n); a(2n) = 3a(2n-1) - a(n).
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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., (ed(AT)mathpuzzle.com), Jan 05 2005)
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CROSSREFS
| Equals 3*A045694(n) for n>0. Cf. A003000, A019309.
Sequence in context: A148559 A108507 A083337 * A000932 A187124 A161006
Adjacent sequences: A019305 A019306 A019307 * A019309 A019310 A019311
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KEYWORD
| nonn
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AUTHOR
| Jeffrey Shallit (shallit(AT)graceland.uwaterloo.ca)
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