A220926 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 columns, 0..3 n X 2 array.

4, 13, 41, 114, 260, 545, 1104, 2182, 4201, 7862, 14295, 25272, 43500, 73013, 119684, 191880, 301285, 463918, 701375, 1042326, 1524300, 2195793, 3118736, 4371362, 6051513, 8280430, 11207071, 15013004, 19917924, 26185845, 34132020, 44130644

Offset

1,1

Comments

Column 2 of A220931.

Links

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

Formula

Empirical: a(n) = (1/20160)*n^8 - (1/2520)*n^7 - (1/1440)*n^6 + (7/45)*n^5 - (3953/2880)*n^4 + (2093/360)*n^3 + (1049/560)*n^2 - (12377/420)*n + 28 for n>3.

Conjectures from Colin Barker, Aug 03 2018: (Start)

G.f.: x*(4 - 23*x + 68*x^2 - 123*x^3 + 122*x^4 - x^5 - 153*x^6 + 172*x^7 - 65*x^8- 8*x^9 + 11*x^10 - 2*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:
..1..1....1..1....0..0....1..1....0..0....0..0....1..1....0..0....1..1....1..1
..1..1....1..1....0..2....1..1....0..1....0..2....1..1....0..1....1..2....1..1
..3..3....1..1....2..3....2..3....1..3....3..3....1..2....1..2....3..3....1..3

Crossrefs

Cf. A220931.

Sequence in context: A222270 A351892 A213496 * A077284 A070428 A320563

Adjacent sequences: A220923 A220924 A220925 * A220927 A220928 A220929

Keyword

nonn

Author

R. H. Hardin, Dec 25 2012

Status

approved