A219167 Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..2 n X 2 array.

3, 7, 23, 53, 103, 182, 302, 478, 728, 1073, 1537, 2147, 2933, 3928, 5168, 6692, 8542, 10763, 13403, 16513, 20147, 24362, 29218, 34778, 41108, 48277, 56357, 65423, 75553, 86828, 99332, 113152, 128378, 145103, 163423, 183437, 205247, 228958, 254678

Offset

1,1

Comments

Column 2 of A219173.

Links

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

Formula

Empirical: a(n) = (1/8)*n^4 - (3/4)*n^3 + (55/8)*n^2 - (49/4)*n + 8 for n>1.

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

G.f.: x*(3 - 8*x + 18*x^2 - 22*x^3 + 13*x^4 - 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....1..0....1..1....0..0....1..1....2..2....0..0....1..1
..1..1....0..0....0..0....0..0....1..1....0..0....1..1....2..2....0..1....1..1
..2..1....2..2....2..0....2..0....1..2....1..2....1..1....2..2....2..1....2..2

Crossrefs

Cf. A219173.

Sequence in context: A205491 A203253 A179491 * A293466 A231722 A168612

Adjacent sequences: A219164 A219165 A219166 * A219168 A219169 A219170

Keyword

nonn

Author

R. H. Hardin, Nov 13 2012

Status

approved