A219454 Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal, vertical, diagonal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..3 n X 2 array.

4, 4, 13, 26, 57, 116, 231, 450, 859, 1604, 2928, 5228, 9139, 15653, 26282, 43275, 69900, 110803, 172457, 263715, 396482, 586522, 854417, 1226696, 1737153, 2428374, 3353494, 4578206, 6183045, 8265971, 10945276, 14362841, 18687770, 24120429

Offset

1,1

Comments

Column 2 of A219460.

Links

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

Formula

Empirical: a(n) = (1/40320)*n^8 - (1/2016)*n^7 + (7/2880)*n^6 + (53/720)*n^5 - (6313/5760)*n^4 + (1961/288)*n^3 - (170417/10080)*n^2 + (3393/280)*n + 13 for n>5.

Conjectures from Colin Barker, Mar 11 2018: (Start)

G.f.: x*(4 - 32*x + 121*x^2 - 283*x^3 + 459*x^4 - 553*x^5 + 525*x^6 - 411*x^7 + 271*x^8 - 149*x^9 + 71*x^10 - 29*x^11 + 8*x^12 - x^13) / (1 - x)^9.

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>14.

(End)

Example

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

Crossrefs

Cf. A219460.

Sequence in context: A099924 A147824 A019081 * A059443 A241250 A097335

Adjacent sequences: A219451 A219452 A219453 * A219455 A219456 A219457

Keyword

nonn

Author

R. H. Hardin, Nov 20 2012

Status

approved