A219621 Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..2 n X 2 array.

3, 11, 27, 56, 105, 183, 301, 472, 711, 1035, 1463, 2016, 2717, 3591, 4665, 5968, 7531, 9387, 11571, 14120, 17073, 20471, 24357, 28776, 33775, 39403, 45711, 52752, 60581, 69255, 78833, 89376, 100947, 113611, 127435, 142488, 158841, 176567, 195741

Offset

1,1

Comments

Column 2 of A219627.

Links

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

Formula

Empirical: a(n) = (1/12)*n^4 + (23/12)*n^2 + n.

Conjectures from Colin Barker, Jul 26 2018: (Start)

G.f.: x*(3 - 4*x + 2*x^2 + x^3) / (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>5.

(End)

Example

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

Crossrefs

Cf. A219627.

Sequence in context: A024194 A011941 A374337 * A033960 A147173 A147110

Adjacent sequences: A219618 A219619 A219620 * A219622 A219623 A219624

Keyword

nonn

Author

R. H. Hardin, Nov 24 2012

Status

approved