A250818 Number of (6+1) X (n+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

13449, 42769, 102393, 207831, 377857, 634509, 1003089, 1512163, 2193561, 3082377, 4216969, 5638959, 7393233, 9527941, 12094497, 15147579, 18745129, 22948353, 27821721, 33432967, 39853089, 47156349, 55420273, 64725651, 75156537, 86800249

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..203

Formula

Empirical: a(n) = 136*n^4 + 1225*n^3 + 4402*n^2 + 5499*n + 2187.

Conjectures from Colin Barker, Nov 21 2018: (Start)

G.f.: x*(13449 - 24476*x + 23038*x^2 - 10934*x^3 + 2187*x^4) / (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>5.

(End)

Example

Some solutions for n=3:
..0..0..0..0....2..2..2..2....1..1..1..0....1..1..1..1....2..1..2..2
..1..1..1..1....0..0..0..0....0..0..0..0....1..1..1..1....1..1..2..2
..2..2..2..2....0..0..0..0....0..0..0..1....2..2..2..2....1..1..2..2
..0..0..0..0....2..2..2..2....1..1..1..2....2..2..2..2....1..1..2..2
..0..0..0..0....1..1..1..1....1..1..1..2....1..1..1..2....1..1..2..2
..2..2..2..2....0..0..1..1....0..0..0..1....0..0..0..1....0..0..1..1
..0..1..2..2....1..1..2..2....0..1..1..2....1..1..1..2....0..0..2..2

Crossrefs

Row 6 of A250812.

Sequence in context: A332387 A183676 A204394 * A271210 A284952 A250616

Adjacent sequences: A250815 A250816 A250817 * A250819 A250820 A250821

Keyword

nonn

Author

R. H. Hardin, Nov 27 2014

Status

approved