A219590 Number of n X 3 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 n X 3 array.

6, 18, 84, 264, 705, 1739, 4129, 9518, 21271, 46019, 96412, 195879, 386603, 742477, 1389545, 2537385, 4526097, 7895059, 13481452, 22558778, 37028253, 59679103, 94537481, 147328016, 226076963, 341891611, 509957092, 750799089, 1091869239

Offset

1,1

Comments

Column 3 of A219595.

Links

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

Formula

Empirical: a(n) = (1/13305600)*n^11 + (1/1814400)*n^10 - (1/48384)*n^9 + (67/120960)*n^8 - (1009/403200)*n^7 + (403/86400)*n^6 + (106961/241920)*n^5 - (1857341/362880)*n^4 + (10083109/302400)*n^3 - (4379099/50400)*n^2 + (889043/9240)*n - 17 for n>2.

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

G.f.: x*(6 - 54*x + 264*x^2 - 876*x^3 + 2091*x^4 - 3619*x^5 + 4579*x^6 - 4324*x^7 + 3206*x^8 - 1982*x^9 + 1025*x^10 - 397*x^11 + 93*x^12 - 9*x^13) / (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>14.

(End)

Example

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

Crossrefs

Cf. A219595.

Sequence in context: A277609 A188119 A239420 * A260664 A279260 A371987

Adjacent sequences: A219587 A219588 A219589 * A219591 A219592 A219593

Keyword

nonn

Author

R. H. Hardin, Nov 23 2012

Status

approved