A250808 Number of (n+1) X (4+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.

441, 1731, 6171, 20631, 66291, 207831, 641571, 1961031, 5955891, 18013431, 54331971, 163579431, 491905491, 1478051031, 4438822371, 13325805831, 39996095091, 120025640631, 360151632771, 1080604320231, 3242111804691

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) = (620*3^n - 570*2^n + 162)/2.

Empirical g.f.: 3*x*(147 - 305*x + 212*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..1..0..0..0....1..1..1..1..1....1..1..1..1..1
..0..0..0..0..1....0..0..0..1..1....0..0..0..0..0....1..1..1..1..1
..0..0..0..0..1....0..0..0..1..1....1..1..1..1..2....0..0..0..1..1
..0..0..1..1..2....1..1..1..2..2....0..0..0..0..1....0..0..0..1..1
..0..0..1..1..2....0..0..0..2..2....0..1..1..1..2....0..0..0..1..1

Crossrefs

Column 4 of A250812.

Sequence in context: A057949 A057950 A343827 * A202400 A014793 A264305

Adjacent sequences: A250805 A250806 A250807 * A250809 A250810 A250811

Keyword

nonn

Author

R. H. Hardin, Nov 27 2014

Status

approved