A253505 Number of (n+2) X (3+2) 0..1 arrays with every 2 X 2 and 3 X 3 subblock diagonal maximum minus antidiagonal minimum nondecreasing horizontally and vertically.

428, 784, 1332, 2088, 3052, 4248, 5692, 7404, 9404, 11712, 14348, 17332, 20684, 24424, 28572, 33148, 38172, 43664, 49644, 56132, 63148, 70712, 78844, 87564, 96892, 106848, 117452, 128724, 140684, 153352, 166748, 180892, 195804, 211504, 228012

Offset

1,1

Links

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

Formula

Empirical: a(n) = (10/3)*n^3 + 64*n^2 + (566/3)*n + 92 for n>4.

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

G.f.: 4*x*(107 - 232*x + 191*x^2 - 62*x^3 - 4*x^4 + 6*x^5 - 2*x^6 + x^7) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>8.

(End)

Example

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

Crossrefs

Column 3 of A253510.

Sequence in context: A224668 A343536 A030467 * A173798 A233812 A231047

Adjacent sequences: A253502 A253503 A253504 * A253506 A253507 A253508

Keyword

nonn

Author

R. H. Hardin, Jan 02 2015

Status

approved