A252933 Number of n X 3 nonnegative integer arrays with upper left 0 and every value within 3 of its king move distance from the upper left and every value increasing by 0 or 1 with every step right, diagonally se or down.

4, 13, 44, 153, 494, 1343, 3016, 5833, 10114, 16179, 24348, 34941, 48278, 64679, 84464, 107953, 135466, 167323, 203844, 245349, 292158, 344591, 402968, 467609, 538834, 616963, 702316, 795213, 895974, 1004919, 1122368, 1248641, 1384058

Offset: 1

Author

R. H. Hardin, Dec 24 2014

Keywords

• nonn

Examples

			Some solutions for n=4:
..0..0..0....0..0..1....0..1..1....0..0..1....0..0..0....0..0..0....0..0..0
..0..0..1....1..1..1....1..1..1....0..1..1....0..0..0....0..0..1....0..0..1
..0..1..1....1..2..2....2..2..2....1..1..1....1..1..1....0..0..1....1..1..1
..0..1..1....1..2..2....2..2..3....1..1..2....1..1..1....1..1..1....1..1..2
		

Links

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

Crossrefs

Column 3 of A252938.

Formula

Empirical: a(n) = (160/3)*n^3 - 548*n^2 + (6071/3)*n - 2591 for n>4.

Conjectures from Colin Barker, Dec 07 2018: (Start)

G.f.: x*(4 - 3*x + 16*x^2 + 39*x^3 + 98*x^4 + 122*x^5 + 40*x^6 + 4*x^7) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>8.

(End)