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

1,1

Comments

Row 3 of A219595.

Links

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

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)

Example

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

Crossrefs

Cf. A219595.

Sequence in context: A108306 A199115 A320649 * A182251 A191597 A088556

Adjacent sequences: A219593 A219594 A219595 * A219597 A219598 A219599

Keyword

nonn

Author

R. H. Hardin, Nov 23 2012

Status

approved