A250855 Number of (3+1) X (n+1) 0..3 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.

2670, 13097, 44797, 123016, 290646, 614965, 1195457, 2172712, 3738406, 6146361, 9724685, 14888992, 22156702, 32162421, 45674401, 63612080, 87064702, 117311017, 155840061, 204373016, 264886150, 339634837, 431178657, 542407576, 676569206

Offset

1,1

Links

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

Formula

Empirical: a(n) = (3/2)*n^6 + (74/3)*n^5 + (621/4)*n^4 + (3161/6)*n^3 + (3691/4)*n^2 + 783*n + 256.

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

G.f.: x*(2670 - 5593*x + 9188*x^2 - 8976*x^3 + 5326*x^4 - 1791*x^5 + 256*x^6) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)

Example

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

Crossrefs

Row 3 of A250853.

Sequence in context: A151813 A010088 A252301 * A235253 A309762 A344192

Adjacent sequences: A250852 A250853 A250854 * A250856 A250857 A250858

Keyword

nonn

Author

R. H. Hardin, Nov 28 2014

Status

approved