A253503 Number of (n+2) X (1+2) 0..1 arrays with every 2 X 2 and 3 X 3 subblock diagonal maximum minus antidiagonal minimum nondecreasing horizontally and vertically.

132, 260, 428, 636, 884, 1172, 1500, 1868, 2276, 2724, 3212, 3740, 4308, 4916, 5564, 6252, 6980, 7748, 8556, 9404, 10292, 11220, 12188, 13196, 14244, 15332, 16460, 17628, 18836, 20084, 21372, 22700, 24068, 25476, 26924, 28412, 29940, 31508, 33116

Offset

1,1

Links

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

Formula

Empirical: a(n) = 20*n^2 + 68*n + 44.

Conjectures from Colin Barker, Dec 16 2018: (Start)

G.f.: 4*x*(33 - 34*x + 11*x^2) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.

(End)

Example

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

Crossrefs

Column 1 of A253510.

Sequence in context: A204649 A224548 A253510 * A195674 A319274 A241754

Adjacent sequences: A253500 A253501 A253502 * A253504 A253505 A253506

Keyword

nonn

Author

R. H. Hardin, Jan 02 2015

Status

approved