A220148 Number of n X 3 arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 n X 3 array.

6, 23, 77, 242, 727, 2062, 5493, 13773, 32664, 73654, 158660, 327852, 652215, 1253089, 2331716, 4212805, 7407330, 12701233, 21278447, 34888718, 56073127, 88463032, 137171407, 209299293, 314584340, 466223256, 681905438, 985101192

Offset

1,1

Comments

Column 3 of A220153.

Links

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

Formula

Empirical: a(n) = (1/19958400)*n^11 + (1/725760)*n^10 + (1/145152)*n^9 + (19/120960)*n^8 + (7/3600)*n^7 + (109/34560)*n^6 + (58081/725760)*n^5 + (26759/181440)*n^4 - (400597/907200)*n^3 + (863/126)*n^2 - (2792/495)*n + 5.

Conjectures from Colin Barker, Jul 30 2018: (Start)

G.f.: x*(6 - 49*x + 197*x^2 - 484*x^3 + 815*x^4 - 997*x^5 + 934*x^6 - 685*x^7 + 389*x^8 - 161*x^9 + 42*x^10 - 5*x^11) / (1 - x)^12.

a(n) = 12*a(n-1) - 66*a(n-2) + 220*a(n-3) - 495*a(n-4) + 792*a(n-5) - 924*a(n-6) + 792*a(n-7) - 495*a(n-8) + 220*a(n-9) - 66*a(n-10) + 12*a(n-11) - a(n-12) for n>12.

(End)

Example

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

Crossrefs

Cf. A220153.

Sequence in context: A060188 A058751 A034359 * A114245 A220238 A078798

Adjacent sequences: A220145 A220146 A220147 * A220149 A220150 A220151

Keyword

nonn

Author

R. H. Hardin, Dec 06 2012

Status

approved