A219211 Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal, vertical, diagonal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..2 n X 2 array.

3, 3, 7, 12, 21, 35, 57, 91, 142, 216, 320, 462, 651, 897, 1211, 1605, 2092, 2686, 3402, 4256, 5265, 6447, 7821, 9407, 11226, 13300, 15652, 18306, 21287, 24621, 28335, 32457, 37016, 42042, 47566, 53620, 60237, 67451, 75297, 83811, 93030, 102992

Offset

1,1

Comments

Column 2 of A219217.

Links

R. H. Hardin, Table of n, a(n) for n = 1..185

Formula

Empirical: a(n) = (1/24)*n^4 - (5/12)*n^3 + (59/24)*n^2 - (37/12)*n + 1 for n>3.

Conjectures from Colin Barker, Mar 11 2018: (Start)

G.f.: x*(3 - 12*x + 22*x^2 - 23*x^3 + 16*x^4 - 8*x^5 + 4*x^6 - x^7) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>6.

(End)

Example

All solutions for n=3:
..0..0....1..1....2..2....1..1....1..1....0..0....0..0
..0..0....1..1....2..2....0..0....1..1....0..0....0..0
..2..2....2..2....2..2....0..0....1..1....1..1....0..0

Crossrefs

Cf. A219217.

Sequence in context: A343752 A068626 A126698 * A088859 A177942 A360873

Adjacent sequences: A219208 A219209 A219210 * A219212 A219213 A219214

Keyword

nonn

Author

R. H. Hardin, Nov 14 2012

Status

approved