A250899 Number of (1+1) X (n+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

37, 127, 403, 1229, 3673, 10875, 32095, 94729, 280069, 829943, 2465227, 7338309, 21883825, 65356531, 195414199, 584800769, 1751256541, 5246953839, 15726181411, 47147086909, 141374151817, 423979849067, 1271637557263, 3814275137529

Offset

1,1

Links

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

Formula

Empirical: a(n) = 9*a(n-1) - 31*a(n-2) + 51*a(n-3) - 40*a(n-4) + 12*a(n-5).

Conjectures from Colin Barker, Nov 23 2018: (Start)

G.f.: x*(37 - 206*x + 407*x^2 - 348*x^3 + 108*x^4) / ((1 - x)^2*(1 - 2*x)^2*(1 - 3*x)).

a(n) = (7 - 2^(4+n) + 3^(3+n) + (2+2^(3+n))*n) / 2.

(End)

Example

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

Crossrefs

Row 1 of A250898.

Sequence in context: A250898 A165811 A142331 * A139734 A142388 A117504

Adjacent sequences: A250896 A250897 A250898 * A250900 A250901 A250902

Keyword

nonn

Author

R. H. Hardin, Nov 28 2014

Status

approved