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A080679
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Lexicographically earliest de Bruijn cycle of length 16 (repeated indefinitely)
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8
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0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0
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OFFSET
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0,1
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REFERENCES
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N. G. de Bruijn, A combinatorial problem, Koninklijke Nederlandse Akademie v. Wetenschappen 49, 758-764, 1946.
S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967, Chap. VI, Section 2.2.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).
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FORMULA
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a(n) = (1/240)*{16*(n mod 16)+[(n+1) mod 16]+[(n+2) mod 16]+[(n+3) mod 16]-14*[(n+4) mod 16]+16*[(n+5) mod 16]-14*[(n+6) mod 16]+16*[(n+7) mod 16]+[(n+8) mod 16]-14*[(n+9) mod 16]+[(n+10) mod 16]+16*[(n+11) mod 16]-14*[(n+12) mod 16]+[(n+13) mod 16]+[(n+14) mod 16]+[(n+15) mod 16]}.
Periodic with period 16.
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EXAMPLE
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The period is 0000100110101111.
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MATHEMATICA
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LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1}, 99] (* Ray Chandler, Aug 26 2015 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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