A253506 Number of (n+2) X (4+2) 0..1 arrays with every 2 X 2 and 3 X 3 subblock diagonal maximum minus antidiagonal minimum nondecreasing horizontally and vertically.

636, 1196, 2088, 3400, 5136, 7396, 10236, 13748, 18024, 23168, 29292, 36516, 44968, 54784, 66108, 79092, 93896, 110688, 129644, 150948, 174792, 201376, 230908, 263604, 299688, 339392, 382956, 430628, 482664, 539328, 600892, 667636, 739848

Offset

1,1

Links

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

Formula

Empirical: a(n) = (1/3)*n^4 + 6*n^3 + (329/3)*n^2 + 288*n - 12 for n>6.

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

G.f.: 4*x*(159 - 496*x + 617*x^2 - 360*x^3 + 59*x^4 + 45*x^5 - 35*x^6 + 20*x^7 - 9*x^8 + 3*x^9 - x^10) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>11.

(End)

Example

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

Crossrefs

Column 4 of A253510.

Sequence in context: A260244 A250581 A061623 * A202048 A251039 A203054

Adjacent sequences: A253503 A253504 A253505 * A253507 A253508 A253509

Keyword

nonn

Author

R. H. Hardin, Jan 02 2015

Status

approved