A250856 Number of (4+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.

12311, 63631, 223933, 626416, 1499679, 3204951, 6279401, 11485528, 19866631, 32808359, 52106341, 80039896, 119451823, 173834271, 247420689, 345283856, 473439991, 638958943, 850080461, 1116336544, 1448679871, 1859618311

Offset

1,1

Links

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

Formula

Empirical: a(n) = (76/9)*n^6 + (1595/12)*n^5 + (28765/36)*n^4 + (31373/12)*n^3 + (155683/36)*n^2 + (10223/3)*n + 1024.

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

G.f.: x*(12311 - 22546*x + 37047*x^2 - 35749*x^3 + 21160*x^4 - 7167*x^5 + 1024*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=2:
..0..0..0....3..3..1....3..1..0....2..2..2....3..3..3....3..2..1....3..3..3
..3..3..3....1..1..1....0..0..0....1..1..1....0..0..0....0..0..0....2..3..3
..1..1..1....2..2..2....0..0..0....1..1..1....0..0..0....2..2..2....1..2..2
..3..3..3....0..1..1....0..0..0....0..3..3....0..0..0....0..0..0....0..1..1
..0..0..0....1..2..3....1..2..2....0..3..3....2..2..2....0..0..0....0..1..1

Crossrefs

Row 4 of A250853.

Sequence in context: A061745 A251776 A045084 * A242716 A077186 A077189

Adjacent sequences: A250853 A250854 A250855 * A250857 A250858 A250859

Keyword

nonn

Author

R. H. Hardin, Nov 28 2014

Status

approved