A253152 Number of (n+1) X (1+1) 0..1 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally and vertically.

16, 39, 69, 109, 181, 325, 613, 1189, 2341, 4645, 9253, 18469, 36901, 73765, 147493, 294949, 589861, 1179685, 2359333, 4718629, 9437221, 18874405, 37748773, 75497509, 150994981, 301989925, 603979813, 1207959589, 2415919141, 4831838245

Offset

1,1

Comments

Column 1 of A253159.

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) + 37 for n>3.

Empirical g.f.: x*(16 - 9*x - 16*x^2 - 20*x^3 - 8*x^4) / ((1 - x)*(1 - 2*x)). - Colin Barker, Mar 20 2018

Example

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

Crossrefs

Cf. A253159.

Sequence in context: A121375 A342976 A347410 * A305362 A197603 A144448

Adjacent sequences: A253149 A253150 A253151 * A253153 A253154 A253155

Keyword

nonn

Author

R. H. Hardin, Dec 28 2014

Status

approved