A169671 -id:A169671 - cp's OEIS frontend

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

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

Offset: 0

N. J. A. Sloane, Mar 03 2003

nonn

			The period is 0000100110101111.

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.

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

Cf. A169671, A169672, A169673, A169674.

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 *)

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.

A169673 Lexicographically earliest de Bruijn sequence for n = 7 and k = 2.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1

Offset: 0

N. J. A. Sloane, Apr 11 2010

			Periodic with period 128, the period being:
00000001000001100001010000111000100100010110001101000111100100110\
010101001011100110110011101001111101010110101111011011101111111

Ray Chandler, Table of n, a(n) for n = 0..1023
Frank Ruskey, Generate de Bruijn sequences
Index entries for linear recurrences with constant coefficients, order 128.

Cf. A021913, A169675, A080679, A169672, A169671, A169674.

A169674 Lexicographically earliest de Bruijn sequence for n = 8 and k = 2.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0

Offset: 0

N. J. A. Sloane, Apr 11 2010

			Periodic with period 256, the period being:
0000000010000001100000101000001110000100100001011000011010000111100010\
0010011000101010001011100011001000110110001110100011111001001010010011\
1001010110010110100101111001100110101001101110011101100111101001111110\
1010101110101101101011111011011110111011111111

Ray Chandler, Table of n, a(n) for n = 0..1023
Frank Ruskey, Generate de Bruijn sequences
Index entries for linear recurrences with constant coefficients, order 256.

Cf. A021913, A169675, A080679, A169672, A169671, A169673.

A169672 Lexicographically earliest de Bruijn sequence for n = 5 and k = 2.

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0

Offset: 0

N. J. A. Sloane, Apr 11 2010

			Periodic with period 32, the period being: 00000100011001010011101011011111.

Frank Ruskey, Generate de Bruijn sequences
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).

Cf. A021913, A169675, A080679, A169671, A169673, A169674.

LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1},{0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1},99] (* Ray Chandler, Aug 26 2015 *)

A169675 Lexicographically earliest de Bruijn sequence for n = 3 and k = 2.

Original entry on oeis.org

0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0

Offset: 0

N. J. A. Sloane, Apr 11 2010

The lexicographically earliest de Bruijn sequence for n = 2 and k = 2 is 0011 repeated (see A021913).

			Periodic with period 8, the period being 00010111.

Frank Ruskey, Generate de Bruijn sequences
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,1).

Cf. A021913, A080679, A169672, A169671, A169673, A169674.

LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 1},{0, 0, 0, 1, 0, 1, 1, 1},99] (* Ray Chandler, Aug 25 2015 *)
PadRight[{},120,{0,0,0,1,0,1,1,1}] (* Harvey P. Dale, Aug 01 2024 *)

A058342 De Bruijn sequence of order 6: every window of size 6, [a(j),a(j+1),...,a(j+5)], shows a different 6-tuple, for 0 <= j <= 63.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1

Offset: 0

Leon J. Tate (leonjtate(AT)earthlink.net), Dec 14 2000

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.6.12.

Index entries for linear recurrences with constant coefficients, signature (1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1).

Cf. A016031. A169671 gives the earliest such sequence.

A169676 Lexicographically earliest de Bruijn sequence for n = 2 and k = 3.

Original entry on oeis.org

0, 0, 1, 0, 2, 1, 1, 2, 2, 0, 0, 1, 0, 2, 1, 1, 2, 2, 0, 0, 1, 0, 2, 1, 1, 2, 2, 0, 0, 1, 0, 2, 1, 1, 2, 2, 0, 0, 1, 0, 2, 1, 1, 2, 2, 0, 0, 1, 0, 2, 1, 1, 2, 2, 0, 0, 1, 0, 2, 1, 1, 2, 2, 0, 0, 1, 0, 2, 1, 1, 2, 2, 0, 0, 1, 0, 2, 1, 1, 2, 2, 0, 0, 1, 0, 2, 1, 1, 2, 2, 0, 0, 1, 0, 2, 1, 1, 2, 2

Offset: 0

N. J. A. Sloane, Apr 11 2010

			Periodic with period 9, the period being 001021122.

Frank Ruskey, Generate de Bruijn sequences
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,1).

Cf. A021913, A169675, A080679, A169672, A169671, A169673, A169674.

LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 1},{0, 0, 1, 0, 2, 1, 1, 2, 2},99] (* Ray Chandler, Aug 26 2015 *)

If someone would like to help, I would like to get analogous entries for k = 3 and n = 3,4,5,6; k = 4 and n = 2,3,4,5,6; k = 5 and n = 2,3,4,5,6; and n = 2 and k = 6,7,8,9, ...

cp's OEIS Frontend

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

Views

Author

Keywords

Examples

References

Links

Crossrefs

Programs

Mathematica

Formula

A169673 Lexicographically earliest de Bruijn sequence for n = 7 and k = 2.

Views

Author

Keywords

Examples

Links

Crossrefs

A169674 Lexicographically earliest de Bruijn sequence for n = 8 and k = 2.

Views

Author

Keywords

Examples

Links

Crossrefs

A169672 Lexicographically earliest de Bruijn sequence for n = 5 and k = 2.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

A169675 Lexicographically earliest de Bruijn sequence for n = 3 and k = 2.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

A058342 De Bruijn sequence of order 6: every window of size 6, [a(j),a(j+1),...,a(j+5)], shows a different 6-tuple, for 0 <= j <= 63.

Views

Author

Keywords

References

Links

Crossrefs

A169676 Lexicographically earliest de Bruijn sequence for n = 2 and k = 3.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

Extensions