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A019309
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Number of "bifix-free" words of length n over a four-letter alphabet.
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4
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1, 4, 12, 48, 180, 720, 2832, 11328, 45132, 180528, 721392, 2885568, 11539440, 46157760, 184619712, 738478848, 2953870260, 11815481040, 47261743632, 189046974528, 756187176720, 3024748706880, 12098991941952
(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) = 4a(2n); a(2n) = 4a(2n-1) - a(n).
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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., (ed(AT)mathpuzzle.com), Jan 05 2005)
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CROSSREFS
| Cf. A003000, A019308, A094547, A094559, A094578.
Sequence in context: A149383 A149384 A108508 * A056632 A149385 A092898
Adjacent sequences: A019306 A019307 A019308 * A019310 A019311 A019312
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KEYWORD
| nonn,easy
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AUTHOR
| Jeffrey Shallit (shallit(AT)graceland.uwaterloo.ca)
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