A219680 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..2 n X 2 array.

3, 4, 9, 19, 35, 60, 98, 154, 234, 345, 495, 693, 949, 1274, 1680, 2180, 2788, 3519, 4389, 5415, 6615, 8008, 9614, 11454, 13550, 15925, 18603, 21609, 24969, 28710, 32860, 37448, 42504, 48059, 54145, 60795, 68043, 75924, 84474, 93730, 103730, 114513

Offset

1,1

Comments

Column 2 of A219686.

Links

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

Formula

Empirical: a(n) = (1/24)*n^4 - (1/4)*n^3 + (47/24)*n^2 - (7/4)*n for n>2.

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

G.f.: x*(3 - 11*x + 19*x^2 - 16*x^3 + 5*x^4 + 2*x^5 - x^6) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>7.

(End)

Example

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

Crossrefs

Cf. A219686.

Sequence in context: A178784 A192288 A028344 * A078010 A291532 A110810

Adjacent sequences: A219677 A219678 A219679 * A219681 A219682 A219683

Keyword

nonn

Author

R. H. Hardin, Nov 25 2012

Status

approved