A250819 Number of (7+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.

41112, 131455, 315561, 641571, 1167796, 1962717, 3104985, 4683421, 6797016, 9554931, 13076497, 17491215, 22938756, 29568961, 37541841, 47027577, 58206520, 71269191, 86416281, 103858651, 123817332, 146523525, 172218601, 201154101

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..126

Formula

Empirical: a(n) = (1695/4)*n^4 + 3786*n^3 + (54287/4)*n^2 + (33539/2)*n + 6561.

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

G.f.: x*(41112 - 74105*x + 69406*x^2 - 32804*x^3 + 6561*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=2:
..1..0..0....1..0..0....1..1..2....2..1..0....1..1..1....0..0..0....2..2..0
..0..0..0....0..0..0....0..0..1....0..0..0....1..1..1....0..0..0....0..0..0
..1..1..1....1..1..2....1..1..2....0..0..0....0..0..0....1..1..1....2..2..2
..1..1..1....0..0..1....0..0..1....0..1..1....0..0..0....2..2..2....2..2..2
..0..0..0....1..1..2....0..0..1....0..1..2....2..2..2....2..2..2....2..2..2
..0..0..0....0..0..1....1..1..2....0..1..2....2..2..2....1..1..1....0..0..0
..1..2..2....0..0..1....1..1..2....0..1..2....0..0..0....0..0..0....0..0..0
..0..2..2....0..0..2....0..1..2....0..1..2....1..1..1....0..0..1....0..1..1

Crossrefs

Row 7 of A250812.

Sequence in context: A237395 A252121 A252118 * A234546 A344456 A257422

Adjacent sequences: A250816 A250817 A250818 * A250820 A250821 A250822

Keyword

nonn

Author

R. H. Hardin, Nov 27 2014

Status

approved