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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A209423 A185784 A185904 * A050339 A087288 A185779

Adjacent sequences:  A201615 A201616 A201617 * A201619 A201620 A201621

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 03 2011

STATUS

approved

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Last modified January 22 16:37 EST 2020. Contains 331152 sequences. (Running on oeis4.)