A186843 Number of (n+1) X 3 binary arrays with no 2 X 2 subblock diagonal sum less antidiagonal sum equal to any horizontal or vertical neighbor 2 X 2 subblock diagonal sum less antidiagonal sum.

50, 218, 970, 4194, 18246, 79778, 347530, 1514138, 6603034, 28783358, 125459410, 546925146, 2384168474, 10392867762, 45304600806, 197491613026, 860900508458, 3752824392746, 16359260883466, 71313013661214, 310866547441298

Offset

1,1

Comments

Column 2 of A186850.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = 2*a(n-1) + 4*a(n-2) + 24*a(n-3) + 14*a(n-4) + 3*a(n-5) + 2*a(n-6).

Empirical g.f.: 2*x*(25 + 59*x + 167*x^2 + 91*x^3 + 23*x^4 + 14*x^5) / (1 - 2*x - 4*x^2 - 24*x^3 - 14*x^4 - 3*x^5 - 2*x^6). - Colin Barker, Apr 19 2018

Example

Some solutions for 5 X 3:
..1..1..0....0..0..1....0..0..0....0..0..1....0..0..1....0..0..0....1..0..0
..1..0..1....0..1..1....0..0..1....0..1..0....1..1..1....0..1..0....0..1..1
..0..0..1....1..0..1....1..0..1....0..0..1....1..0..1....0..1..1....0..0..1
..0..0..0....0..1..0....0..1..0....0..1..0....0..1..1....0..0..0....1..1..1
..1..0..1....1..1..1....1..1..1....1..1..1....1..0..0....0..0..1....0..1..1

Crossrefs

Cf. A186850.

Sequence in context: A273293 A097371 A179755 * A250527 A251065 A231087

Adjacent sequences: A186840 A186841 A186842 * A186844 A186845 A186846

Keyword

nonn

Author

R. H. Hardin, Feb 27 2011

Status

approved