A219817 Number of 3 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..2 3 X n array.

6, 16, 62, 165, 377, 795, 1588, 3039, 5612, 10061, 17603, 30184, 50875, 84444, 138160, 222896, 354610, 556296, 860511, 1312599, 1974749, 2931041, 4293652, 6210413, 8873928, 12532487, 17503027, 24186418, 33085375, 44825322, 60178560, 80092118

Offset

1,1

Comments

Row 3 of A219816.

Links

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

Formula

Empirical: a(n) = (1/362880)*n^9 - (1/40320)*n^8 + (13/60480)*n^7 + (1/2880)*n^6 + (305/3456)*n^5 - (1927/5760)*n^4 + (25129/45360)*n^3 + (58243/3360)*n^2 - (135179/2520)*n + 58 for n>3.

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

G.f.: x*(6 - 44*x + 172*x^2 - 455*x^3 + 857*x^4 - 1142*x^5 + 1051*x^6 - 640*x^7 + 242*x^8 - 48*x^9 - x^10 + 4*x^11 - x^12) / (1 - x)^10.

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>13.

(End)

Example

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

Crossrefs

Cf. A219816.

Sequence in context: A091649 A125628 A078672 * A120795 A118640 A277747

Adjacent sequences: A219814 A219815 A219816 * A219818 A219819 A219820

Keyword

nonn

Author

R. H. Hardin, Nov 28 2012

Status

approved