A184130 Number of n X 2 0..2 arrays with rows and columns in nondecreasing order.

6, 29, 112, 356, 972, 2359, 5217, 10704, 20647, 37818, 66287, 111865, 182651, 289698, 447814, 676515, 1001148, 1454203, 2076834, 2920610, 4049518, 5542241, 7494735, 10023130, 13266981, 17392896, 22598569, 29117247, 37222661, 47234452, 59524124

Offset

1,1

Comments

Column 2 of A184137.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) (=polynomial of degree 8).

Conjectures from Colin Barker, Apr 12 2018: (Start)

G.f.: x*(2 - x)*(3 - 11*x + 28*x^2 - 42*x^3 + 39*x^4 - 22*x^5 + 7*x^6 - x^7) / (1 - x)^9.

a(n) = (40320 + 79344*n + 64140*n^2 + 37884*n^3 + 16009*n^4 + 3696*n^5 + 490*n^6 + 36*n^7 + n^8) / 40320.

(End)

Example

Some solutions for 3 X 2:
..0..1....1..2....0..2....0..1....0..0....0..1....0..0....0..2....0..1....0..2
..0..1....2..0....1..1....0..2....0..2....1..2....0..0....2..1....1..2....2..1
..2..2....2..1....1..2....2..2....0..2....2..2....0..2....2..1....2..0....2..2

Crossrefs

Cf. A184137.

Sequence in context: A100874 A047923 A006816 * A326805 A061648 A281050

Adjacent sequences: A184127 A184128 A184129 * A184131 A184132 A184133

Keyword

nonn

Author

R. H. Hardin, Jan 09 2011

Status

approved