A219810 Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal, vertical or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 n X 2 array.

3, 6, 16, 33, 61, 106, 176, 281, 433, 646, 936, 1321, 1821, 2458, 3256, 4241, 5441, 6886, 8608, 10641, 13021, 15786, 18976, 22633, 26801, 31526, 36856, 42841, 49533, 56986, 65256, 74401, 84481, 95558, 107696, 120961, 135421, 151146, 168208, 186681

Offset

1,1

Comments

Column 2 of A219816.

Links

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

Formula

Empirical: a(n) = (1/12)*n^4 - (1/2)*n^3 + (41/12)*n^2 - 3*n + 1 for n>1.

Conjectures from Colin Barker, Jul 28 2018: (Start)

G.f.: x*(3 - 9*x + 16*x^2 - 17*x^3 + 11*x^4 - 2*x^5) / (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

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

Crossrefs

Cf. A219816.

Sequence in context: A308401 A196261 A229180 * A364319 A122742 A052370

Adjacent sequences: A219807 A219808 A219809 * A219811 A219812 A219813

Keyword

nonn

Author

R. H. Hardin, Nov 28 2012

Status

approved