A219472 Number of 2 X n arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..3 2 X n array.

10, 23, 68, 211, 547, 1248, 2663, 5432, 10666, 20206, 36984, 65512, 112528, 187831, 305340, 484415, 751481, 1141999, 1702831, 2495049, 3597241, 5109370, 7157245, 9897666, 13524308, 18274412, 24436354, 32358166, 42457086, 55230217, 71266378

Offset

1,1

Comments

Row 2 of A219471.

Links

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

Formula

Empirical: a(n) = (1/13440)*n^8 + (1/10080)*n^7 + (1/576)*n^6 + (119/720)*n^5 - (9659/5760)*n^4 + (18247/1440)*n^3 - (50047/2016)*n^2 + (6437/840)*n + 13 for n>3.

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

G.f.: x*(10 - 67*x + 221*x^2 - 413*x^3 + 424*x^4 - 153*x^5 - 91*x^6 + 35*x^7 + 124*x^8 - 129*x^9 + 49*x^10 - 7*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:
..2..2..2....2..2..2....0..0..1....1..1..1....2..2..2....1..1..1....0..0..1
..2..2..2....2..1..1....1..0..0....1..1..1....2..0..0....1..2..2....1..3..3

Crossrefs

Cf. A219471.

Sequence in context: A262485 A219940 A164578 * A196890 A219383 A250188

Adjacent sequences: A219469 A219470 A219471 * A219473 A219474 A219475

Keyword

nonn

Author

R. H. Hardin, Nov 20 2012

Status

approved