A213119 Number of binary arrays of length 2*n+1 with fewer than n ones in any length 2n subsequence (=less than 50% duty cycle).

1, 7, 34, 151, 646, 2710, 11236, 46231, 189214, 771442, 3136156, 12720982, 51507964, 208260556, 841065544, 3393346711, 13679459854, 55106773786, 221860011244, 892741834546, 3590659699444, 14436037598836, 58018598086264

Offset

1,2

Comments

Row 2 of A213118.

Links

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

Formula

Recurrence: n*a(n) = 2*(4*n-3)*a(n-1) - 8*(2*n-3)*a(n-2). - Vaclav Kotesovec, Oct 19 2012

G.f.: 1/(1-4*x)-3/(2*sqrt(1-4*x)). - Vaclav Kotesovec, Oct 21 2012

a(n) = 4^n - 3*C(2*n-1,n). - Vaclav Kotesovec, Oct 29 2012

Example

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

Mathematica

Table[4^n-3*Binomial[2*n-1, n], {n, 1, 20}] (* Vaclav Kotesovec, Oct 29 2012 *)

Crossrefs

Sequence in context: A080960 A243414 A335087 * A099242 A032206 A124466

Adjacent sequences: A213116 A213117 A213118 * A213120 A213121 A213122

Keyword

nonn

Author

R. H. Hardin, Jun 05 2012

Status

approved