A253226 Number of (n+1) X (3+1) 0..1 arrays with every 2 X 2 subblock diagonal minimum minus antidiagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal maximum nondecreasing vertically.

125, 306, 494, 914, 1709, 3241, 6231, 12122, 23800, 47037, 93377, 185908, 370806, 740423, 1479463, 2957334, 5912852, 11823649, 23644989, 47287400, 94571938, 189140715, 378277955, 756552106, 1513100064, 3026195621, 6052386361

Offset

1,1

Links

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

Formula

Empirical: a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4) for n>8.

Conjectures from Colin Barker, Dec 10 2018: (Start)

G.f.: x*(125 - 319*x + 89*x^2 + 323*x^3 - 307*x^4 + 76*x^5 - 3*x^6 + x^7) / ((1 - x)^3*(1 - 2*x)).

a(n) = 46 + 1443*2^(n-5) + (13*n)/2 + (15*n^2)/2 for n>4.

(End)

Example

Some solutions for n=4:
..0..0..0..0....1..0..0..1....1..1..1..1....0..1..0..1....0..0..0..0
..1..1..0..0....1..0..0..0....0..0..0..0....0..1..0..0....0..0..0..0
..1..1..0..0....1..0..0..0....1..1..1..1....1..1..0..0....1..1..1..1
..1..1..0..0....1..0..0..0....0..0..0..0....1..1..0..0....1..0..0..0
..0..0..0..1....1..0..0..1....0..1..1..1....1..0..0..0....1..0..0..1

Crossrefs

Column 3 of A253231.

Sequence in context: A023079 A172460 A338469 * A223182 A256362 A175486

Adjacent sequences: A253223 A253224 A253225 * A253227 A253228 A253229

Keyword

nonn

Author

R. H. Hardin, Dec 29 2014

Status

approved