A219687 Number of 3 X n arrays of the minimum value of corresponding elements and their horizontal, vertical or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 3 X n array.

6, 9, 31, 87, 208, 452, 922, 1799, 3394, 6234, 11196, 19713, 34085, 57937, 96878, 159429, 258304, 412146, 647840, 1003547, 1532627, 2308645, 3431682, 5036203, 7300766, 10459890, 14818436, 20768893, 28812001, 39581185, 53871318, 72672377

Offset

1,1

Comments

Row 3 of A219686.

Links

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

Formula

Empirical: a(n) = (1/181440)*n^9 - (1/4032)*n^8 + (31/4320)*n^7 - (37/288)*n^6 + (14137/8640)*n^5 - (7859/576)*n^4 + (3420947/45360)*n^3 - (240133/1008)*n^2 + (63709/180)*n - 79 for n>6.

Conjectures from Colin Barker, Jul 26 2018: (Start)

G.f.: x*(6 - 51*x + 211*x^2 - 538*x^3 + 913*x^4 - 1055*x^5 + 824*x^6 - 413*x^7 + 110*x^8 + 8*x^9 - 27*x^10 + 23*x^11 - 12*x^12 + x^13 + 3*x^14 - x^15) / (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>15.

(End)

Example

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

Crossrefs

Cf. A219686.

Sequence in context: A179908 A180325 A192425 * A147415 A217048 A105866

Adjacent sequences: A219684 A219685 A219686 * A219688 A219689 A219690

Keyword

nonn

Author

R. H. Hardin, Nov 25 2012

Status

approved