A250815 Number of (3+1) X (n+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.

432, 1315, 3081, 6171, 11116, 18537, 29145, 43741, 63216, 88551, 120817, 161175, 210876, 271261, 343761, 429897, 531280, 649611, 786681, 944371, 1124652, 1329585, 1561321, 1822101, 2114256, 2440207, 2802465, 3203631, 3646396, 4133541, 4667937

Offset

1,1

Links

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

Formula

Empirical: a(n) = (15/4)*n^4 + 36*n^3 + (527/4)*n^2 + (359/2)*n + 81.

Conjectures from Colin Barker, Nov 21 2018: (Start)

G.f.: x*(432 - 845*x + 826*x^2 - 404*x^3 + 81*x^4) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

(End)

Example

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

Crossrefs

Row 3 of A250812.

Sequence in context: A231231 A179666 A203663 * A006910 A015229 A360840

Adjacent sequences: A250812 A250813 A250814 * A250816 A250817 A250818

Keyword

nonn

Author

R. H. Hardin, Nov 27 2014

Status

approved