A201618 Number of n X 1 0..3 arrays with rows and columns lexicographically nondecreasing and every element equal to at least one horizontal or vertical neighbor.

0, 4, 4, 10, 16, 26, 40, 59, 84, 116, 156, 205, 264, 334, 416, 511, 620, 744, 884, 1041, 1216, 1410, 1624, 1859, 2116, 2396, 2700, 3029, 3384, 3766, 4176, 4615, 5084, 5584, 6116, 6681, 7280, 7914, 8584, 9291, 10036, 10820, 11644, 12509, 13416, 14366, 15360

Offset

1,2

Comments

Column 1 of A201625.

Links

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

Formula

Empirical: a(n) = (1/6)*n^3 - n^2 + (35/6)*n - 9 for n>4.

For n > 4 the above empirical a(n) is equal to C(n-1,3) + 4C(n-2,1) that is the n-th coefficient in Taylor series of ((1-x+x^2)/(1-x))^4 at x=0. - Nikita Gogin, Jul 24 2013

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

G.f.: x^2*(2 - 2*x + x^2)*(2 - 4*x + 4*x^2 - 2*x^3 + x^4) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>8.

(End)

Example

Some solutions for n=10:
..1....0....0....2....1....1....1....0....0....0....0....1....2....0....0....0
..1....0....0....2....1....1....1....0....0....0....0....1....2....0....0....0
..1....0....2....2....1....1....1....0....0....1....1....1....3....0....1....0
..1....1....2....2....1....2....1....0....0....1....1....2....3....0....1....0
..2....1....3....2....1....2....1....0....1....3....1....2....3....0....2....2
..2....2....3....2....1....2....1....0....1....3....1....2....3....3....2....2
..2....2....3....2....1....3....2....2....1....3....1....2....3....3....3....2
..2....2....3....2....1....3....2....2....2....3....1....2....3....3....3....2
..2....3....3....3....2....3....3....2....2....3....1....2....3....3....3....2
..2....3....3....3....2....3....3....2....2....3....1....2....3....3....3....2

Crossrefs

Sequence in context: A357620 A185784 A185904 * A341243 A050339 A087288

Adjacent sequences: A201615 A201616 A201617 * A201619 A201620 A201621

Keyword

nonn

Author

R. H. Hardin, Dec 03 2011

Status

approved