A250758 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 x(i,j)+x(i-1,j) in the j direction.

332, 756, 1353, 2123, 3066, 4182, 5471, 6933, 8568, 10376, 12357, 14511, 16838, 19338, 22011, 24857, 27876, 31068, 34433, 37971, 41682, 45566, 49623, 53853, 58256, 62832, 67581, 72503, 77598, 82866, 88307, 93921, 99708, 105668, 111801, 118107

Offset

1,1

Links

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

Formula

Empirical: a(n) = (173/2)*n^2 + (329/2)*n + 81.

Conjectures from Colin Barker, Nov 18 2018: (Start)

G.f.: x*(332 - 240*x + 81*x^2) / (1 - x)^3.

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

(End)

Example

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

Crossrefs

Row 3 of A250755.

Sequence in context: A231755 A097401 A376734 * A114084 A257892 A235020

Adjacent sequences: A250755 A250756 A250757 * A250759 A250760 A250761

Keyword

nonn

Author

R. H. Hardin, Nov 27 2014

Status

approved