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

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*n-19)*a(n) = 2*(28*n^2-97*n+60)*a(n-1) - 8*(2*n-5)*(7*n-12) * a(n-2). - Vaclav Kotesovec, Oct 19 2012

a(n) = 2^(2*n+2) - 5*(7*n-4)*C(2*n-2,n-1)/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*n-4)*Binomial[2*n-2, n-1]/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