A212730 Number of 0..2 arrays of length 2*n with sum less than 2*n in any length 2n subsequence (=less than 50% duty cycle)

3, 31, 294, 2727, 25048, 228826, 2083371, 18925047, 171633840, 1554702516, 14069962041, 127240600050, 1150026301089, 10389276050527, 93819553163854, 846952848390039, 7643713441711560, 68967751709641564, 622154460094492809

Offset

1,1

Comments

Row 1 of A212729

Links

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

Formula

From Vaclav Kotesovec, Jul 31 2013: (Start)

Empirical: n*(2*n-1)*(16*n^2 - 60*n + 53)*a(n) = (608*n^4 - 3032*n^3 + 5050*n^2 - 3259*n + 660)*a(n-1) - 9*(352*n^4 - 2008*n^3 + 3986*n^2 - 3143*n + 750)*a(n-2) + 81*(n-2)*(2*n-5)*(16*n^2 - 28*n + 9)*a(n-3).

Conjecture: a(n) ~ 9^n/2. (End)

Example

Some solutions for n=3
..0....2....0....0....0....2....0....2....2....1....1....1....2....1....1....2
..0....0....0....0....0....1....1....0....0....1....2....0....0....0....1....2
..1....0....0....0....0....0....0....0....0....0....0....2....1....0....0....0
..1....0....1....2....0....0....2....1....0....2....0....0....1....0....0....1
..0....0....2....1....1....0....1....0....1....1....0....0....1....1....1....0
..1....1....1....2....2....1....0....1....2....0....0....1....0....2....0....0

Crossrefs

Sequence in context: A242134 A221894 A198964 * A236957 A112425 A144579

Adjacent sequences: A212727 A212728 A212729 * A212731 A212732 A212733

Keyword

nonn

Author

R. H. Hardin May 25 2012

Status

approved