A220198 Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal, vertical or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..3 n X 2 array.

4, 10, 38, 103, 245, 547, 1168, 2395, 4724, 8982, 16504, 29381, 50797, 85475, 140254, 224821, 352624, 541994, 817506, 1211611, 1766573, 2536747, 3591236, 5016967, 6922228, 9440710, 12736100, 17007273, 22494133, 29484155, 38319682, 49406033

Offset

1,1

Comments

Column 2 of A220204.

Links

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

Formula

Empirical: a(n) = (1/20160)*n^8 - (1/5040)*n^7 - (1/480)*n^6 + (107/720)*n^5 - (1151/960)*n^4 + (278/45)*n^3 - (54427/5040)*n^2 + (5323/420)*n - 7 for n>1.

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

G.f.: x*(4 - 26*x + 92*x^2 - 215*x^3 + 350*x^4 - 386*x^5 + 277*x^6 - 119*x^7 + 29*x^8 - 4*x^9) / (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>10.

(End)

Example

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

Crossrefs

Cf. A220204.

Sequence in context: A197551 A046562 A240382 * A197051 A149191 A149192

Adjacent sequences: A220195 A220196 A220197 * A220199 A220200 A220201

Keyword

nonn

Author

R. H. Hardin, Dec 07 2012

Status

approved