A220004 Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal, vertical or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..3 n X 2 array.

4, 7, 20, 58, 141, 308, 637, 1271, 2460, 4624, 8444, 14989, 25888, 43557, 71492, 114640, 179861, 276495, 417049, 618020, 900871, 1293178, 1829967, 2555261, 3523858, 4803362, 6476490, 8643679, 11426018, 14968531, 19443838, 25056222

Offset

1,1

Comments

Column 2 of A220010.

Links

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

Formula

Empirical: a(n) = (1/40320)*n^8 - (1/10080)*n^7 - (1/2880)*n^6 + (43/720)*n^5 - (2873/5760)*n^4 + (3893/1440)*n^3 - (1121/1120)*n^2 - (10301/840)*n + 18 for n>3.

Conjectures from Colin Barker, Jul 29 2018: (Start)

G.f.: x*(4 - 29*x + 101*x^2 - 206*x^3 + 255*x^4 - 175*x^5 + 43*x^6 + 14*x^7 + 3*x^8 - 15*x^9 + 7*x^10 - x^11) / (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>12.

(End)

Example

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

Crossrefs

Cf. A220010.

Sequence in context: A026570 A111955 A244791 * A367911 A368185 A359603

Adjacent sequences: A220001 A220002 A220003 * A220005 A220006 A220007

Keyword

nonn

Author

R. H. Hardin, Dec 03 2012

Status

approved