

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
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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(n1,3) + 4C(n2,1) that is the nth coefficient in Taylor series of ((1x+x^2)/(1x))^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(n1)  6*a(n2) + 4*a(n3)  a(n4) 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



