A253430 Number of (n+1) X (3+1) 0..1 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally, vertically and ne-to-sw antidiagonally.

69, 70, 85, 121, 193, 337, 625, 1201, 2353, 4657, 9265, 18481, 36913, 73777, 147505, 294961, 589873, 1179697, 2359345, 4718641, 9437233, 18874417, 37748785, 75497521, 150994993, 301989937, 603979825, 1207959601, 2415919153, 4831838257

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>4.

Empirical: a(n) = 9*2^(n-1) + 49 for n>2.

Empirical g.f.: x*(69 - 137*x + 13*x^2 + 6*x^3) / ((1 - x)*(1 - 2*x)). - Colin Barker, Dec 12 2018

Example

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

Crossrefs

Column 3 of A253435.

Sequence in context: A033389 A265189 A345486 * A256694 A166067 A253437

Adjacent sequences: A253427 A253428 A253429 * A253431 A253432 A253433

Keyword

nonn

Author

R. H. Hardin, Dec 31 2014

Status

approved