The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A263656

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A263656

Number of length-2n central circular binary strings without zigzags (see reference for precise definition).
(history; published version)

#23 by Wesley Ivan Hurt at Sun Oct 08 09:56:55 EDT 2017

STATUS

reviewed

approved

#22 by Michel Marcus at Sun Oct 08 09:52:35 EDT 2017

STATUS

proposed

reviewed

#21 by Jon E. Schoenfield at Sun Oct 08 09:37:22 EDT 2017

STATUS

editing

proposed

#20 by Jon E. Schoenfield at Sun Oct 08 09:37:19 EDT 2017

FORMULA

a(n) = (1/n)*(3*(n-1)*a(n-1) - 4*(n-4)*a(n-2) + (7*n-27)*a(n-3) - 6*a(n-4) + (7*n-37)*a(n-5) - 3*(n-6)*a(n-6)) for n >= 6. - Andrew Howroyd, Feb 26 2017

#19 by Jon E. Schoenfield at Sun Oct 08 09:36:55 EDT 2017

FORMULA

a(n)=(1/n)*(3*(n-1)*a(n-1) - 4*(n-4)*a(n-2) + (7*n-27)*a(n-3) - 6*a(n-4) + (7*n-37)*a(n-5) - 3*(n-6)*a(n-6)) for n >= 6. - Andrew Howroyd, Feb 26 2017

STATUS

proposed

editing

#18 by Jean-François Alcover at Sun Oct 08 09:30:02 EDT 2017

STATUS

editing

proposed

#17 by Jean-François Alcover at Sun Oct 08 09:29:56 EDT 2017

MATHEMATICA

a[n_ /; n < 6] := {0, 0, 4, 6, 12, 30}[[n + 1]]; a[n_] := a[n] = (-(3*(n - 6)*a[n - 6]) + (7*n - 37)*a[n - 5] - 6*a[n - 4] + (7*n - 27)*a[n - 3] - 4*(n - 4)*a[n - 2] + 3*(n - 1)*a[n - 1])/n;

Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Oct 08 2017, after Andrew Howroyd *)

STATUS

approved

editing

#16 by N. J. A. Sloane at Sun Feb 26 21:09:46 EST 2017

STATUS

proposed

approved

#15 by Andrew Howroyd at Sun Feb 26 20:12:29 EST 2017

STATUS

editing

proposed

Discussion

Sun Feb 26

21:09

N. J. A. Sloane: > Since this is published, do you want me to re-add the original sequence as an erroneous version of this one? Me:  YES, ABSOLUTELY!! Please do!

#14 by Andrew Howroyd at Sun Feb 26 19:02:51 EST 2017

FORMULA

a(n)=(1/n)*(3*(n-1)*a(n-1) - 4*(n-4)*a(n-2) + (7*n-27)*a(n-3) - 6*a(n-4) + (7*n-37)*a(n-5) - 3*(n-6)*a(n-6)) for n>=6. _- _Andrew Howroyd_, Feb 26 2017

Discussion

Sun Feb 26

19:58

Andrew Howroyd: The reference shows the sequence as starting 0, 2, 4, 6, 12 which seems to be a misprint (page 6 - central strings). However, fig 1 shows the correct values with this sequence as main diagonal. Also recurrence they provide matches this sequence - in short this is certainly just a misprint. Since this is published, do you want me to re-add the original sequence as an erroneous version of this one?