

A213121


Number of binary arrays of length 2*n+3 with fewer than n ones in any length 2n subsequence (=less than 50% duty cycle).


1



1, 14, 86, 424, 1926, 8404, 35836, 150604, 626726, 2589844, 10646676, 43594464, 177950236, 724578824, 2944375096, 11944652884, 48388816486, 195794585044, 791434666276, 3196307541904, 12898839944116, 52019043912664
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OFFSET

1,2


COMMENTS

Row 4 of A213118.


LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210


FORMULA

Recurrence: n*(7*n19)*a(n) = 2*(28*n^297*n+60)*a(n1)  8*(2*n5)*(7*n12) * a(n2).  Vaclav Kotesovec, Oct 19 2012
a(n) = 2^(2*n+2)  5*(7*n4)*C(2*n2,n1)/n.  Vaclav Kotesovec, Oct 29 2012


EXAMPLE

Some solutions for n=3
..0....0....1....0....0....0....0....0....0....0....1....1....1....1....0....1
..0....0....0....0....0....1....0....1....1....0....1....0....0....0....0....0
..1....1....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....1....0....0....0....1....0....1....0....0....0....0....0....1
..1....0....1....0....1....1....0....0....1....1....0....0....0....0....0....0
..0....0....0....0....1....0....0....0....0....0....0....0....1....0....0....0
..0....0....0....0....0....0....0....0....0....0....1....0....0....1....0....0
..0....1....0....1....0....0....0....0....0....0....0....1....1....0....1....0
..0....1....1....0....0....1....0....0....0....0....0....1....0....0....1....0


MATHEMATICA

Table[2^(2*n+2)5*(7*n4)*Binomial[2*n2, n1]/n, {n, 1, 20}] (* Vaclav Kotesovec, Oct 29 2012 *)


CROSSREFS

Sequence in context: A244865 A059600 A206621 * A125324 A126482 A206614
Adjacent sequences: A213118 A213119 A213120 * A213122 A213123 A213124


KEYWORD

nonn


AUTHOR

R. H. Hardin, Jun 05 2012


STATUS

approved



