A250854 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 min(x(i,j),x(i-1,j)) in the j direction.

543, 2457, 8037, 21436, 49599, 103293, 198297, 356752, 608671, 993609, 1562493, 2379612, 3524767, 5095581, 7209969, 10008768, 13658527, 18354457, 24323541, 31827804, 41167743, 52685917, 66770697, 83860176, 104446239, 129078793

Offset

1,1

Links

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

Formula

Empirical: a(n) = (2/9)*n^6 + (47/12)*n^5 + (953/36)*n^4 + (1141/12)*n^3 + (6527/36)*n^2 + 172*n + 64.

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

G.f.: x*(543 - 1344*x + 2241*x^2 - 2231*x^3 + 1334*x^4 - 447*x^5 + 64*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:
..2..2..1..1..1....2..1..0..0..0....3..3..3..1..2....3..2..3..1..1
..1..1..1..1..1....0..0..1..1..2....0..0..0..0..1....0..0..1..1..1
..2..3..3..3..3....0..0..1..2..3....1..2..2..2..3....0..0..2..2..2

Crossrefs

Row 2 of A250853.

Sequence in context: A163764 A268146 A074888 * A250685 A051305 A204732

Adjacent sequences: A250851 A250852 A250853 * A250855 A250856 A250857

Keyword

nonn

Author

R. H. Hardin, Nov 28 2014

Status

approved