A201533 Number of n X 2 0..2 arrays with rows and columns lexicographically nondecreasing and every element equal to at least one horizontal or vertical neighbor.

3, 9, 25, 69, 175, 410, 899, 1859, 3649, 6840, 12311, 21378, 35964, 58819, 93800, 146222, 223292, 334639, 492954, 714755, 1021293, 1439616, 2003809, 2756429, 3750155, 5049674, 6733825, 8898024, 11656994, 15147825, 19533390, 25006144

Offset: 1

Author

R. H. Hardin, Dec 02 2011

Keywords

• nonn

Comments

Column 2 of A201539.

Examples

			Some solutions for n=10:
..0..2....0..2....0..1....0..0....0..1....0..2....0..0....0..0....0..1....0..1
..0..2....0..2....0..1....0..1....0..1....0..2....0..0....0..1....0..1....0..1
..0..2....0..2....1..1....1..1....0..1....2..0....0..0....0..1....0..1....0..1
..0..2....0..2....1..2....1..1....0..1....2..0....0..2....0..2....1..0....0..1
..0..2....0..2....1..2....1..2....1..0....2..0....1..2....0..2....1..0....1..0
..1..1....1..0....1..2....1..2....1..0....2..0....1..2....0..2....1..0....1..0
..1..1....1..0....1..2....2..1....1..0....2..2....2..2....0..2....1..1....2..2
..1..2....2..0....2..0....2..1....2..1....2..2....2..2....2..1....2..1....2..2
..1..2....2..0....2..0....2..2....2..1....2..2....2..2....2..1....2..2....2..2
..1..2....2..2....2..2....2..2....2..2....2..2....2..2....2..1....2..2....2..2
		

Links

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

Crossrefs

Cf. A201539.

Formula

Empirical: a(n) = (1/40320)*n^8 - (1/3360)*n^7 + (23/2880)*n^6 - (1/48)*n^5 + (247/5760)*n^4 + (231/160)*n^3 - (6777/1120)*n^2 + (3121/168)*n - 20 for n>3.

Conjectures from Colin Barker, May 23 2018: (Start)

G.f.: x*(3 - 18*x + 52*x^2 - 84*x^3 + 76*x^4 - 25*x^5 - 19*x^6 + 20*x^7 + x^8 - 9*x^9 + 5*x^10 - x^11) / (1 - x)^9.

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) for n>12.

(End)