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Revision History for A212408

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A212408

Number of binary arrays of length 2*n+6 with no more than n ones in any length 2n subsequence (=50% duty cycle).
(history; published version)

#18 by Susanna Cuyler at Sat May 11 02:21:31 EDT 2019

STATUS

reviewed

approved

#17 by Michel Marcus at Sat May 11 02:10:21 EDT 2019

STATUS

proposed

reviewed

#16 by Michel Marcus at Sat May 11 02:10:15 EDT 2019

STATUS

editing

proposed

#15 by Michel Marcus at Sat May 11 02:10:12 EDT 2019

COMMENTS

Row 7 of A212402.

CROSSREFS

Row 7 of A212402.

STATUS

reviewed

editing

#14 by Joerg Arndt at Sat May 11 01:37:01 EDT 2019

STATUS

proposed

reviewed

#13 by Jon E. Schoenfield at Sat May 11 01:11:14 EDT 2019

STATUS

editing

proposed

#12 by Jon E. Schoenfield at Sat May 11 01:11:11 EDT 2019

NAME

Number of binary arrays of length 2*n+6 with no more than n ones in any length 2n subsequence (=50% duty cycle).

COMMENTS

Row 7 of A212402.

FORMULA

Empirical (for n>=4): a(n) = 2^(2*n+5) - 4*(955*n^3 - 3782*n^2 + 3475*n + 30) * C(2*n-7, n-4) / ((n-2)*(n-1)*n). - Vaclav Kotesovec, Nov 20 2012

EXAMPLE

Some solutions for n=3:

.. 0.... 0.... 0.... 1.... 1.... 0.... 1.... 0.... 0.... 1.... 0.... 1.... 1.... 0.... 1.... 1

.. 0.... 0.... 1.... 0.... 0.... 0.... 0.... 0.... 1.... 0.... 1.... 0.... 0.... 0.... 0.... 0

.. 0.... 1.... 0.... 0.... 0.... 0.... 1.... 1.... 1.... 0.... 1.... 0.... 1.... 0.... 1.... 0

.. 1.... 0.... 1.... 1.... 1.... 0.... 0.... 1.... 0.... 0.... 0.... 1.... 0.... 1.... 0.... 1

.. 0.... 0.... 0.... 0.... 1.... 0.... 1.... 0.... 0.... 1.... 0.... 0.... 0.... 0.... 0.... 1

.. 0.... 0.... 0.... 0.... 0.... 0.... 0.... 0.... 0.... 0.... 0.... 1.... 0.... 0.... 0.... 0

.. 0.... 0.... 0.... 1.... 1.... 1.... 0.... 1.... 1.... 0.... 0.... 0.... 1.... 1.... 0.... 0

.. 0.... 1.... 0.... 0.... 0.... 0.... 0.... 0.... 0.... 0.... 1.... 1.... 1.... 0.... 0.... 0

.. 1.... 0.... 0.... 0.... 0.... 1.... 1.... 1.... 0.... 0.... 1.... 0.... 0.... 0.... 1.... 0

.. 1.... 0.... 0.... 1.... 1.... 0.... 1.... 1.... 0.... 0.... 0.... 1.... 0.... 1.... 0.... 0

.. 0.... 1.... 0.... 0.... 0.... 0.... 0.... 0.... 1.... 1.... 0.... 0.... 1.... 0.... 1.... 0

.. 1.... 0.... 1.... 1.... 1.... 0.... 1.... 0.... 1.... 1.... 1.... 1.... 0.... 0.... 0.... 0

MAPLE

with(gfun): A212408:= rectoproc({a(3)=1314, a(4)=5769, n*(955*n^3-8481*n^2+21998*n-14262)*a(n) = 2*(3820*n^4-36789*n^3+110342*n^2-99213*n-1890)*a(n-1) - 8*(2*n-9)*(955*n^3-5616*n^2+7901*n+210)*a(n-2)}, a(n), remember): 55, 285, seq(A212408(n), n=3..20); A212408(210); - _# _Vaclav Kotesovec_, Nov 20 2012

AUTHOR

R. H. Hardin , May 14 2012

STATUS

approved

editing

#11 by T. D. Noe at Tue Nov 20 11:17:55 EST 2012

STATUS

editing

approved

#10 by T. D. Noe at Tue Nov 20 11:17:51 EST 2012

MAPLE

#verified first terms (holds for all n<=210). - _Vaclav Kotesovec_, Nov 20 2012

STATUS

proposed

editing

#9 by Vaclav Kotesovec at Tue Nov 20 08:11:11 EST 2012

STATUS

editing

proposed