A219940 Number of 2 X n 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..3 2 X n array.

10, 23, 64, 196, 459, 918, 1660, 2802, 4499, 6952, 10416, 15208, 21715, 30402, 41820, 56614, 75531, 99428, 129280, 166188, 211387, 266254, 332316, 411258, 504931, 615360, 744752, 895504, 1070211, 1271674, 1502908, 1767150, 2067867, 2408764

Offset

1,1

Comments

Row 2 of A219939.

Links

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

Formula

Empirical: a(n) = (1/15)*n^5 - (3/4)*n^4 + (32/3)*n^3 - (135/4)*n^2 + (1583/30)*n - 34 for n>2.

Conjectures from Colin Barker, Jul 29 2018: (Start)

G.f.: x*(10 - 37*x + 76*x^2 - 43*x^3 - 67*x^4 + 109*x^5 - 51*x^6 + 11*x^7) / (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>8.

(End)

Example

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

Crossrefs

Cf. A219939.

Sequence in context: A266080 A316093 A262485 * A164578 A219472 A196890

Adjacent sequences: A219937 A219938 A219939 * A219941 A219942 A219943

Keyword

nonn

Author

R. H. Hardin, Dec 01 2012

Status

approved