A250660 Number of (6+1) X (n+1) 0..1 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.

319, 574, 893, 1276, 1723, 2234, 2809, 3448, 4151, 4918, 5749, 6644, 7603, 8626, 9713, 10864, 12079, 13358, 14701, 16108, 17579, 19114, 20713, 22376, 24103, 25894, 27749, 29668, 31651, 33698, 35809, 37984, 40223, 42526, 44893, 47324, 49819, 52378, 55001

Offset

1,1

Links

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

Formula

Empirical: a(n) = 32*n^2 + 159*n + 128.

Conjectures from Colin Barker, Nov 15 2018: (Start)

G.f.: x*(319 - 383*x + 128*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..1..1..1....1..1..1..1..1....0..0..0..0..0....1..1..0..0..0
..1..1..1..1..1....0..0..0..0..0....1..1..1..1..1....0..0..0..0..0
..0..0..0..0..0....0..0..0..0..0....1..1..1..1..1....1..1..1..1..1
..0..0..0..0..0....0..0..0..0..0....1..1..1..1..1....0..0..0..0..0
..1..1..1..1..1....0..0..0..0..0....1..1..1..1..1....0..0..0..0..0
..0..0..0..0..1....1..1..1..1..1....1..1..1..1..1....1..1..1..1..1
..0..0..0..0..1....0..1..1..1..1....1..1..1..1..1....0..0..0..0..0

Crossrefs

Row 6 of A250656.

Sequence in context: A126838 A153048 A053020 * A252410 A064905 A293921

Adjacent sequences: A250657 A250658 A250659 * A250661 A250662 A250663

Keyword

nonn

Author

R. H. Hardin, Nov 26 2014

Status

approved