A250878 Number of (1+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.

90, 288, 678, 1328, 2306, 3680, 5518, 7888, 10858, 14496, 18870, 24048, 30098, 37088, 45086, 54160, 64378, 75808, 88518, 102576, 118050, 135008, 153518, 173648, 195466, 219040, 244438, 271728, 300978, 332256, 365630, 401168, 438938, 479008, 521446

Offset

1,1

Links

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

Formula

Empirical: a(n) = (34/3)*n^3 + 28*n^2 + (104/3)*n + 16.

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

G.f.: 2*x*(45 - 36*x + 33*x^2 - 8*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:
..3..3..2..3..3....2..1..1..1..1....2..2..3..3..3....2..2..2..1..0
..0..0..1..2..2....0..1..1..1..3....1..1..2..2..3....1..1..1..2..3

Crossrefs

Row 1 of A250877.

Sequence in context: A363729 A255784 A250877 * A027621 A331259 A245866

Adjacent sequences: A250875 A250876 A250877 * A250879 A250880 A250881

Keyword

nonn

Author

R. H. Hardin, Nov 28 2014

Status

approved