A250817 Number of (5+1) X (n+1) 0..2 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.

4356, 13735, 32745, 66291, 120304, 201741, 318585, 479845, 695556, 976779, 1335601, 1785135, 2339520, 3013921, 3824529, 4788561, 5924260, 7250895, 8788761, 10559179, 12584496, 14888085, 17494345, 20428701, 23717604, 27388531, 31469985

Offset

1,1

Links

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

Formula

Empirical: a(n) = (171/4)*n^4 + 390*n^3 + (5627/4)*n^2 + (3575/2)*n + 729.

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

G.f.: x*(4356 - 8045*x + 7630*x^2 - 3644*x^3 + 729*x^4) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

(End)

Example

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

Crossrefs

Row 5 of A250812.

Sequence in context: A239193 A068292 A185796 * A154084 A285040 A203928

Adjacent sequences: A250814 A250815 A250816 * A250818 A250819 A250820

Keyword

nonn

Author

R. H. Hardin, Nov 27 2014

Status

approved