A253006 Number of n X 3 nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 3 and every value increasing by 0 or 1 with every step right, diagonally se or down.

0, 0, 0, 1, 54, 632, 2902, 8416, 18770, 35564, 60398, 94872, 140586, 199140, 272134, 361168, 467842, 593756, 740510, 909704, 1102938, 1321812, 1567926, 1842880, 2148274, 2485708, 2856782, 3263096, 3706250, 4187844, 4709478, 5272752, 5879266

Offset

1,5

Links

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

Formula

Empirical: a(n) = (800/3)*n^3 - 3980*n^2 + (60442/3)*n - 34576 for n>6.

Conjectures from Colin Barker, Dec 08 2018: (Start)

G.f.: x^4*(1 + 50*x + 422*x^2 + 694*x^3 + 385*x^4 + 44*x^5 + 4*x^6) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>10.

(End)

Example

Some solutions for n=6:
..0..0..0....0..0..0....0..1..2....0..1..2....0..0..1....0..0..0....0..0..1
..0..0..0....1..1..1....1..1..2....1..1..2....0..1..1....0..0..1....0..0..1
..0..0..1....1..1..1....1..2..2....1..2..2....1..1..2....1..1..1....0..1..1
..0..1..1....1..1..1....1..2..2....1..2..2....2..2..2....1..1..2....1..1..2
..0..1..1....1..2..2....1..2..2....2..2..2....2..2..2....1..2..2....1..1..2
..1..1..2....1..2..2....1..2..2....2..2..2....2..2..2....2..2..2....1..1..2

Crossrefs

Column 3 of A253011.

Sequence in context: A254701 A086577 A193152 * A128961 A218130 A321635

Adjacent sequences: A253003 A253004 A253005 * A253007 A253008 A253009

Keyword

nonn

Author

R. H. Hardin, Dec 25 2014

Status

approved