A250806 Number of (n+1) X (2+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.

100, 379, 1315, 4321, 13735, 42769, 131455, 400681, 1214695, 3669409, 11058895, 33278041, 100036855, 300516049, 902359135, 2708699401, 8129342215, 24394514689, 73196520175, 219615512761, 658898442775, 1976799137329

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) = (126*3^n - 99*2^n + 20)/2.

Empirical g.f.: x*(100 - 221*x + 141*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). - Colin Barker, Nov 20 2018

Example

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

Crossrefs

Column 2 of A250812.

Sequence in context: A138668 A017174 A202334 * A250853 A017270 A105089

Adjacent sequences: A250803 A250804 A250805 * A250807 A250808 A250809

Keyword

nonn

Author

R. H. Hardin, Nov 27 2014

Status

approved