A220147 Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 n X 2 array.

3, 11, 26, 52, 95, 163, 266, 416, 627, 915, 1298, 1796, 2431, 3227, 4210, 5408, 6851, 8571, 10602, 12980, 15743, 18931, 22586, 26752, 31475, 36803, 42786, 49476, 56927, 65195, 74338, 84416, 95491, 107627, 120890, 135348, 151071, 168131, 186602

Offset

1,1

Comments

Column 2 of A220153.

Links

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

Formula

Empirical: a(n) = (1/12)*n^4 - (1/6)*n^3 + (29/12)*n^2 + (2/3)*n.

Conjectures from Colin Barker, Jul 30 2018: (Start)

G.f.: x*(3 - 4*x + x^2 + 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....1..1....0..1....1..1....0..0....1..1....2..2....0..0....0..0
..0..0....0..0....2..1....0..0....0..1....2..2....2..2....2..2....0..0....1..0
..2..2....0..0....2..2....2..2....0..0....2..2....2..2....2..2....1..1....2..2

Crossrefs

Cf. A220153.

Sequence in context: A051925 A211811 A011942 * A256315 A290513 A101612

Adjacent sequences: A220144 A220145 A220146 * A220148 A220149 A220150

Keyword

nonn

Author

R. H. Hardin, Dec 06 2012

Status

approved