A219884 Number of 3 X n arrays of the minimum value of corresponding elements and their horizontal, diagonal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 3 X n array.

10, 21, 47, 129, 292, 600, 1158, 2148, 3863, 6784, 11679, 19763, 32938, 54144, 87860, 140803, 222883, 348483, 538145, 820756, 1236342, 1839593, 2704258, 3928566, 5641847, 8012546, 11257843, 15655113, 21555482, 29399758, 39737040, 53246333

Offset: 1

Author

R. H. Hardin, Nov 30 2012

Keywords

• nonn

Comments

Row 3 of A219883.

Examples

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

Links

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

Crossrefs

Cf. A219883.

Formula

Empirical: a(n) = (1/362880)*n^9 - (1/13440)*n^8 + (17/12096)*n^7 - (37/2880)*n^6 + (1813/17280)*n^5 + (1579/5760)*n^4 - (76849/9072)*n^3 + (768487/10080)*n^2 - (590021/2520)*n + 217 for n>6.

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

G.f.: x*(10 - 79*x + 287*x^2 - 596*x^3 + 697*x^4 - 265*x^5 - 504*x^6 + 984*x^7 - 895*x^8 + 565*x^9 - 351*x^10 + 273*x^11 - 206*x^12 + 112*x^13 - 36*x^14 + 5*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>16.

(End)