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A080679 Lexicographically earliest de Bruijn cycle of length 16 (repeated indefinitely).

%I A080679 #15 Jun 02 2025 00:15:27
%S A080679 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,
%T A080679 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,
%U A080679 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
%N A080679 Lexicographically earliest de Bruijn cycle of length 16 (repeated indefinitely).
%D A080679 N. G. de Bruijn, A combinatorial problem, Koninklijke Nederlandse Akademie v. Wetenschappen 49, 758-764, 1946.
%D A080679 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967, Chap. VI, Section 2.2.
%H A080679 Alex Bogomolny, <a href="http://www.cut-the-knot.com/ctk/FromLCarrollToArchimedes.shtml">Lewis Carroll to Archimedes</a>
%H A080679 F. R. K. Chung, P. Diaconis and R. L. Graham, <a href="https://doi.org/10.1016/0012-365X(92)90699-G">Universal cycles for combinatorial structures</a>, Discr. Math., 110 (1992), 43-59.
%H A080679 Frank Ruskey, <a href="http://combos.org/necklace">Generate Necklaces</a>
%H A080679 <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).
%F A080679 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]}.
%F A080679 Periodic with period 16.
%e A080679 The period is 0000100110101111.
%t A080679 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 *)
%Y A080679 Cf. A169671, A169672, A169673, A169674.
%K A080679 nonn
%O A080679 0,1
%A A080679 _N. J. A. Sloane_, Mar 03 2003