A253391 Number of (n+1) X (2+1) 0..1 arrays with every 2 X 2 subblock antidiagonal maximum minus diagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal minimum nondecreasing vertically.

44, 102, 143, 197, 250, 320, 391, 477, 564, 666, 769, 887, 1006, 1140, 1275, 1425, 1576, 1742, 1909, 2091, 2274, 2472, 2671, 2885, 3100, 3330, 3561, 3807, 4054, 4316, 4579, 4857, 5136, 5430, 5725, 6035, 6346, 6672, 6999, 7341, 7684, 8042, 8401, 8775, 9150

Offset

1,1

Links

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

Formula

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

Empirical for n mod 2 = 0: a(n) = 4*n^2 + (45/2)*n + 41 for n>4.

Empirical for n mod 2 = 1: a(n) = 4*n^2 + (45/2)*n + (75/2) for n>4.

Empirical g.f.: x*(44 + 14*x - 61*x^2 - x^3 + 16*x^4 + 4*x^5 + 2*x^6 - 2*x^7) / ((1 - x)^3*(1 + x)). - Colin Barker, Dec 11 2018

Example

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

Crossrefs

Column 2 of A253397.

Sequence in context: A044563 A129289 A039527 * A050944 A332590 A187933

Adjacent sequences: A253388 A253389 A253390 * A253392 A253393 A253394

Keyword

nonn

Author

R. H. Hardin, Dec 31 2014

Status

approved