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

1,1

Comments

Column 2 of A201539.

Links

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

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)

Example

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

Crossrefs

Cf. A201539.

Sequence in context: A236570 A338726 A323362 * A000242 A077846 A005322

Adjacent sequences: A201530 A201531 A201532 * A201534 A201535 A201536

Keyword

nonn

Author

R. H. Hardin, Dec 02 2011

Status

approved