A253504 Number of (n+2) X (2+2) 0..1 arrays with every 2 X 2 and 3X3 subblock diagonal maximum minus antidiagonal minimum nondecreasing horizontally and vertically.

260, 472, 784, 1196, 1712, 2340, 3088, 3964, 4976, 6132, 7440, 8908, 10544, 12356, 14352, 16540, 18928, 21524, 24336, 27372, 30640, 34148, 37904, 41916, 46192, 50740, 55568, 60684, 66096, 71812, 77840, 84188, 90864, 97876, 105232, 112940, 121008

Offset

1,1

Links

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

Formula

Empirical: a(n) = (4/3)*n^3 + 36*n^2 + (332/3)*n + 92 for n>2.

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

G.f.: 4*x*(65 - 142*x + 114*x^2 - 37*x^3 + x^4 + x^5) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>6.

(End)

Example

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

Crossrefs

Column 2 of A253510.

Sequence in context: A344238 A344237 A139408 * A154379 A185793 A237631

Adjacent sequences: A253501 A253502 A253503 * A253505 A253506 A253507

Keyword

nonn

Author

R. H. Hardin, Jan 02 2015

Status

approved