A250757 Number of (2+1) X (n+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)+x(i-1,j) in the j direction.

105, 237, 423, 663, 957, 1305, 1707, 2163, 2673, 3237, 3855, 4527, 5253, 6033, 6867, 7755, 8697, 9693, 10743, 11847, 13005, 14217, 15483, 16803, 18177, 19605, 21087, 22623, 24213, 25857, 27555, 29307, 31113, 32973, 34887, 36855, 38877, 40953, 43083

Offset

1,1

Links

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

Formula

Empirical: a(n) = 27*n^2 + 51*n + 27.

Conjectures from Colin Barker, Nov 18 2018: (Start)

G.f.: 3*x*(35 - 26*x + 9*x^2) / (1 - x)^3.

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

(End)

Example

Some solutions for n=4:
..1..1..1..1..1....2..2..2..2..2....1..2..2..2..2....1..2..2..2..2
..0..1..1..1..1....0..0..1..1..1....0..2..2..2..2....1..2..2..2..2
..0..1..1..1..1....0..0..2..2..2....0..2..2..2..2....0..1..1..2..2

Crossrefs

Row 2 of A250755.

Sequence in context: A229094 A307108 A262723 * A350199 A146257 A075764

Adjacent sequences: A250754 A250755 A250756 * A250758 A250759 A250760

Keyword

nonn

Author

R. H. Hardin, Nov 27 2014

Status

approved