A220205 Number of 2 X n 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..3 2 X n array.

4, 10, 36, 89, 182, 333, 567, 918, 1431, 2164, 3190, 4599, 6500, 9023, 12321, 16572, 21981, 28782, 37240, 47653, 60354, 75713, 94139, 116082, 142035, 172536, 208170, 249571, 297424, 352467, 415493, 487352, 568953, 661266, 765324, 882225, 1013134

Offset

1,1

Comments

Row 2 of A220204.

Links

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

Formula

Empirical: a(n) = (1/60)*n^5 - (1/8)*n^4 + (11/6)*n^3 - (7/8)*n^2 + (3/20)*n for n>1.

Conjectures from Colin Barker, Jul 31 2018: (Start)

G.f.: x*(4 - 14*x + 36*x^2 - 57*x^3 + 48*x^4 - 18*x^5 + 3*x^6) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>7.

(End)

Example

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

Crossrefs

Cf. A220204.

Sequence in context: A108596 A204270 A287220 * A196880 A359688 A358212

Adjacent sequences: A220202 A220203 A220204 * A220206 A220207 A220208

Keyword

nonn

Author

R. H. Hardin, Dec 07 2012

Status

approved