A219846 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 nonincreasing columns, 0..2 n X 2 array.

3, 7, 16, 33, 62, 108, 177, 276, 413, 597, 838, 1147, 1536, 2018, 2607, 3318, 4167, 5171, 6348, 7717, 9298, 11112, 13181, 15528, 18177, 21153, 24482, 28191, 32308, 36862, 41883, 47402, 53451, 60063, 67272, 75113, 83622, 92836, 102793, 113532, 125093

Offset

1,1

Comments

Column 2 of A219852.

Links

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

Formula

Empirical: a(n) = (1/24)*n^4 + (1/12)*n^3 + (23/24)*n^2 - (1/12)*n + 2.

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

G.f.: x*(3 - 8*x + 11*x^2 - 7*x^3 + 2*x^4) / (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....1..1....0..0....1..1....1..1....1..1....0..0....1..1
..0..1....0..0....1..2....0..0....0..1....1..1....0..0....0..0....0..2....1..1
..1..2....0..0....2..2....0..0....0..0....1..2....0..1....0..2....2..2....1..1

Crossrefs

Cf. A219852.

Sequence in context: A161810 A318604 A084631 * A229914 A192968 A277968

Adjacent sequences: A219843 A219844 A219845 * A219847 A219848 A219849

Keyword

nonn

Author

R. H. Hardin, Nov 29 2012

Status

approved