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Revision History for A212405

(Underlined text is an addition; strikethrough text is a deletion.)

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A212405 Number of binary arrays of length 2*n+3 with no more than n ones in any length 2n subsequence (=50% duty cycle)
(history; published version)
#10 by Joerg Arndt at Mon Oct 29 02:53:32 EDT 2012
STATUS

proposed

approved

#9 by Vaclav Kotesovec at Sun Oct 28 19:21:40 EDT 2012
STATUS

editing

proposed

#8 by Vaclav Kotesovec at Sun Oct 28 19:21:26 EDT 2012
FORMULA

EmpiricalRecurrence (for n>3): n^2*a(n) = 2*(4*n^2-3*n-5)*a(n-1) - 8*(n+1)*(2*n-5)*a(n-2). - Vaclav Kotesovec, Oct 19 2012

a(n) = 2^(2*n+2) - (3*n+1)/n * C(2*n-2,n-1), for n>1. - Vaclav Kotesovec, Oct 28 2012

MATHEMATICA

Flatten[{13, Table[2^(2*n+2)-(3*n+1)/n*Binomial[2*n-2, n-1], {n, 2, 20}]}] (* Vaclav Kotesovec, Oct 28 2012 *)

STATUS

approved

editing

#7 by T. D. Noe at Fri Oct 19 11:57:52 EDT 2012
STATUS

proposed

approved

#6 by Vaclav Kotesovec at Fri Oct 19 09:22:08 EDT 2012
STATUS

editing

proposed

#5 by Vaclav Kotesovec at Fri Oct 19 09:22:02 EDT 2012
FORMULA

Empirical (for n>3): n^2*a(n) = 2*(4*n^2-3*n-5)*a(n-1) - 8*(n+1)*(2*n-5)*a(n-2). - Vaclav Kotesovec, Oct 19 2012

STATUS

approved

editing

#4 by R. H. Hardin at Mon May 14 22:14:48 EDT 2012
STATUS

editing

approved

#3 by R. H. Hardin at Mon May 14 22:14:39 EDT 2012
LINKS

R. H. Hardin, <a href="/A212405/b212405.txt">Table of n, a(n) for n = 1..210</a>

#2 by R. H. Hardin at Mon May 14 22:14:09 EDT 2012
NAME

allocated for R. H. Hardin

Number of binary arrays of length 2*n+3 with no more than n ones in any length 2n subsequence (=50% duty cycle)

DATA

13, 57, 236, 959, 3872, 15586, 62632, 251419, 1008536, 4043582, 16206152, 64933782, 260114976, 1041797124, 4171943056, 16704821779, 66880877896, 267747443494, 1071808583176, 4290243456514, 17172082337536, 68729504287324

OFFSET

1,1

COMMENTS

Row 4 of A212402

EXAMPLE

Some solutions for n=3

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

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

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

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

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

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

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

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

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

KEYWORD

allocated

nonn

AUTHOR

R. H. Hardin May 14 2012

STATUS

approved

editing

#1 by R. H. Hardin at Mon May 14 21:59:03 EDT 2012
NAME

allocated for R. H. Hardin

KEYWORD

allocated

STATUS

approved

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Last modified August 18 13:06 EDT 2024. Contains 375269 sequences. (Running on oeis4.)