A250807 Number of (n+1) X (3+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.

225, 873, 3081, 10233, 32745, 102393, 315561, 963513, 2924265, 8840313, 26656041, 80238393, 241255785, 724848633, 2176708521, 6534450873, 19612003305, 58853311353, 176594537001, 529852816953, 1589696862825, 4769367412473

Offset

1,1

Links

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

Formula

Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3); a(n) = (304*3^n - 264*2^n + 66)/2.

Empirical g.f.: 3*x*(75 - 159*x + 106*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). - Colin Barker, Nov 20 2018

Example

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

Crossrefs

Column 3 of A250812.

Sequence in context: A352518 A027470 A134934 * A330096 A091078 A272674

Adjacent sequences: A250804 A250805 A250806 * A250808 A250809 A250810

Keyword

nonn

Author

R. H. Hardin, Nov 27 2014

Status

approved