A169675 -id:A169675 - cp's OEIS frontend

A169671 Lexicographically earliest de Bruijn sequence for n = 6 and k = 2.

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

Offset: 0

N. J. A. Sloane, Apr 11 2010

			Periodic with period 64, the period being:
0000001000011000101000111001001011001101001111010101110110111111.

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

See A058342 for another version.

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 *)

A140427 Arises in relating doubly-even error-correcting codes, graphs and irreducible representations of N-extended supersymmetry.

Original entry on oeis.org

0, 0, 0, 0, 1, 1, 2, 3, 4, 4, 4, 4, 5, 5, 6, 7, 8, 8, 8, 8, 9, 9, 10, 11, 12, 12, 12, 12, 13, 13, 14, 15, 16, 16, 16, 16, 17, 17, 18, 19, 20, 20, 20, 20, 21, 21, 22, 23, 24, 24, 24, 24, 25, 25, 26, 27, 28, 28, 28, 28, 29, 29, 30

Offset: 0

Jonathan Vos Post, Jun 18 2008

Conjecture: essentially partial sums of A169675 (verified for n <= 10000). - Sean A. Irvine, Jul 19 2022

Nathaniel Johnston, Table of n, a(n) for n = 0..10000
C. F. Doran, M. G. Faux, S. J. Gates Jr, T. Hubsch, K. M. Iga and G. D. Landweber, Relating Doubly-Even Error-Correcting Codes, Graphs and Irreducible Representations of N-Extended Supersymmetry, arXiv:0806.0051 [hep-th], 2008. See formula (13) on page 6.

A140427 := proc(n) local l: l:=[0, 0, 0, 0, 1, 1, 2, 3]: if(n<=7)then return l[n+1]:else return l[(n mod 8) + 1] + 4*floor(n/8): fi: end:
seq(A140427(n),n=0..62); # Nathaniel Johnston, Apr 26 2011

a[n_] := Module[{L = {0, 0, 0, 0, 1, 1, 2, 3}}, If[n <= 7, L[[n + 1]], L[[Mod[n, 8] + 1]] + 4*Floor[n/8]]];
Table[a[n], {n, 0, 62}] (* Jean-François Alcover, Nov 28 2017, from Maple *)

a(n) = 0 for 0 <= n < 4, a(n) = floor(((n-4)^2)/4)+1 for n = 4, 5, 6, 7, and a(n) = a(n-8) + 4 for n>7.

G.f.: x^4*(x^4+x^3+x^2+1) / ((x-1)^2*(x+1)*(x^2+1)*(x^4+1)). - Colin Barker, May 04 2013

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, ...

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A169671 Lexicographically earliest de Bruijn sequence for n = 6 and k = 2.

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

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

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

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A140427 Arises in relating doubly-even error-correcting codes, graphs and irreducible representations of N-extended supersymmetry.

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

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