A253154 Number of (n+1) X (3+1) 0..1 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally and vertically.

69, 88, 94, 129, 201, 345, 633, 1209, 2361, 4665, 9273, 18489, 36921, 73785, 147513, 294969, 589881, 1179705, 2359353, 4718649, 9437241, 18874425, 37748793, 75497529, 150995001, 301989945, 603979833, 1207959609, 2415919161, 4831838265

Offset

1,1

Links

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

Formula

Empirical: a(n) = 3*a(n-1) - 2*a(n-2) for n>5.

Empirical: a(n) = 9*2^(n-1) + 57 for n>3.

Empirical g.f.: x*(69 - 119*x - 32*x^2 + 23*x^3 + 2*x^4) / ((1 - x)*(1 - 2*x)). - Colin Barker, Dec 09 2018

Example

Some solutions for n=6:
..0..0..0..0....0..0..0..0....0..0..0..0....0..1..1..1....0..0..0..0
..0..0..0..0....1..1..1..1....1..1..1..1....0..0..0..0....0..0..0..0
..0..0..0..0....0..0..0..0....1..1..1..1....1..1..1..1....0..0..0..0
..0..0..0..0....0..0..0..0....0..0..0..0....1..1..1..1....0..0..0..0
..0..0..0..0....1..1..1..1....1..1..1..1....0..0..0..0....1..1..1..1
..1..1..1..1....0..0..0..0....1..1..1..1....1..1..1..1....0..0..0..0
..1..1..1..1....0..0..0..1....1..1..1..1....0..0..0..0....0..0..0..1

Crossrefs

Column 3 of A253159.

Sequence in context: A045021 A254712 A197172 * A140368 A039434 A043257

Adjacent sequences: A253151 A253152 A253153 * A253155 A253156 A253157

Keyword

nonn

Author

R. H. Hardin, Dec 28 2014

Status

approved