A258555 Number of (2+1) X (n+1) 0..1 arrays with every 2 X 2 subblock ne-sw antidiagonal difference nondecreasing horizontally and nw+se diagonal sum nondecreasing vertically.

44, 112, 210, 344, 506, 683, 894, 1140, 1421, 1725, 2071, 2460, 2892, 3355, 3868, 4432, 5047, 5701, 6413, 7184, 8014, 8891, 9834, 10844, 11921, 13053, 14259, 15540, 16896, 18315, 19816, 21400, 23067, 24805, 26633, 28552, 30562, 32651, 34838, 37124, 39509

Offset

1,1

Links

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

Formula

Empirical: a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-4) - 3*a(n-5) + 3*a(n-6) - a(n-7) for n>10.

Empirical g.f.: x*(44 - 20*x + 6*x^2 + 6*x^3 - 52*x^4 + 7*x^5 + 13*x^6 - 5*x^7 + 8*x^8 + x^9) / ((1 - x)^4*(1 + x)*(1 + x^2)). - Colin Barker, Dec 22 2018

Example

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

Crossrefs

Row 2 of A258554.

Sequence in context: A118483 A044231 A044612 * A258548 A036198 A094128

Adjacent sequences: A258552 A258553 A258554 * A258556 A258557 A258558

Keyword

nonn

Author

R. H. Hardin, Jun 03 2015

Status

approved