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

1,1

Links

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

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)

Example

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

Crossrefs

Column 3 of A252938.

Sequence in context: A073717 A149427 A290907 * A229397 A283110 A149428

Adjacent sequences: A252930 A252931 A252932 * A252934 A252935 A252936

Keyword

nonn

Author

R. H. Hardin, Dec 24 2014

Status

approved