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A080679 Lexicographically earliest de Bruijn cycle of length 16 (repeated indefinitely) 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

REFERENCES

N. G. de Bruijn, A combinatorial problem, Koninklijke Nederlandse Akademie v. Wetenschappen 49, 758-764, 1946.

F. R. K. Chung, P. Diaconis and R. L. Graham, Universal cycles for combinatorial structures, Discr. Math., 110 (1992), 43-59.

S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967, Chap. VI, Section 2.2.

LINKS

Table of n, a(n) for n=0..98.

Alex Bogomolny, Lewis Carroll to Archimedes

Frank Ruskey, Generate Necklaces

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).

FORMULA

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.

EXAMPLE

The period is 0000100110101111.

MATHEMATICA

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 *)

CROSSREFS

Cf. A169671, A169672, A169673, A169674.

Sequence in context: A011664 A179831 A094091 * A144193 A171387 A011662

Adjacent sequences:  A080676 A080677 A080678 * A080680 A080681 A080682

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Mar 03 2003

STATUS

approved

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Last modified January 15 20:47 EST 2019. Contains 319184 sequences. (Running on oeis4.)