A250879 Number of (2+1) X (n+1) 0..3 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.

440, 1456, 3442, 6728, 11644, 18520, 27686, 39472, 54208, 72224, 93850, 119416, 149252, 183688, 223054, 267680, 317896, 374032, 436418, 505384, 581260, 664376, 755062, 853648, 960464, 1075840, 1200106, 1333592, 1476628, 1629544, 1792670

Offset

1,1

Links

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

Formula

Empirical: a(n) = 55*n^3 + 155*n^2 + 166*n + 64.

Conjectures from Colin Barker, Nov 22 2018: (Start)

G.f.: 2*x*(220 - 152*x + 129*x^2 - 32*x^3) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.

(End)

Example

Some solutions for n=4:
..1..1..1..1..1....2..2..2..2..0....3..3..3..3..3....2..2..2..2..2
..2..2..2..2..3....1..1..1..1..3....1..1..1..2..2....2..2..3..3..3
..1..1..1..1..3....0..0..0..1..3....0..1..1..2..3....0..1..3..3..3

Crossrefs

Row 2 of A250877.

Sequence in context: A279950 A072604 A158319 * A247722 A234202 A061626

Adjacent sequences: A250876 A250877 A250878 * A250880 A250881 A250882

Keyword

nonn

Author

R. H. Hardin, Nov 28 2014

Status

approved