A219596 Number of 3 X n arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 3 X n array.

6, 21, 84, 233, 550, 1188, 2415, 4684, 8746, 15833, 27945, 48286, 81907, 136629, 224336, 362747, 577797, 906780, 1402432, 2138159, 3214644, 4768098, 6980453, 10091830, 14415652, 20356811, 28433339, 39302076, 53788873, 72923915, 97982798

Offset: 1

Author

R. H. Hardin, Nov 23 2012

Keywords

• nonn

Comments

Row 3 of A219595.

Examples

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

Links

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

Crossrefs

Cf. A219595.

Formula

Empirical: a(n) = (1/181440)*n^9 - (1/8064)*n^8 + (11/3780)*n^7 - (107/2880)*n^6 + (749/1728)*n^5 - (1943/1152)*n^4 + (168241/90720)*n^3 + (355057/10080)*n^2 - (306913/2520)*n + 137 for n>3.

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

G.f.: x*(6 - 39*x + 144*x^2 - 382*x^3 + 740*x^4 - 1009*x^5 + 933*x^6 - 554*x^7 + 195*x^8 - 32*x^9 - 5*x^10 + 7*x^11 - 2*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)