A250754 Number of (n+1) X (7+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.

527, 1707, 5471, 17211, 53327, 163467, 497471, 1506651, 4548527, 13702827, 41223071, 123898491, 372154127, 1117379787, 3353974271, 10065592731, 30204118127, 90627034347, 271910463071, 815790109371, 2447487768527

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) = (468*3^n - 224*2^n + 98)/2.

Empirical g.f.: x*(527 - 1455*x + 1026*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). - Colin Barker, Nov 17 2018

Example

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

Crossrefs

Column 7 of A250755.

Sequence in context: A153660 A337779 A261075 * A158364 A232885 A085329

Adjacent sequences: A250751 A250752 A250753 * A250755 A250756 A250757

Keyword

nonn

Author

R. H. Hardin, Nov 27 2014

Status

approved