A252999 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 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.

0, 0, 0, 1, 34, 279, 1028, 2601, 5318, 9499, 15464, 23533, 34026, 47263, 63564, 83249, 106638, 134051, 165808, 202229, 243634, 290343, 342676, 400953, 465494, 536619, 614648, 699901, 792698, 893359, 1002204, 1119553, 1245726, 1381043, 1525824

Offset

1,5

Links

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

Formula

Empirical: a(n) = (160/3)*n^3 - 708*n^2 + (9539/3)*n - 4831 for n>4.

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

G.f.: x^4*(1 + 30*x + 149*x^2 + 112*x^3 + 28*x^4) / (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=6:
..0..0..0....0..1..1....0..1..2....0..0..1....0..0..1....0..0..1....0..1..1
..0..0..1....1..1..2....1..1..2....0..1..1....0..1..1....1..1..1....1..1..2
..0..0..1....1..2..2....1..1..2....0..1..2....1..1..1....1..1..1....1..1..2
..1..1..1....2..2..2....1..2..2....1..1..2....1..1..2....1..1..2....1..1..2
..1..1..2....2..2..2....1..2..2....1..2..2....2..2..2....1..2..2....1..2..2
..2..2..2....2..2..2....2..2..2....2..2..2....2..2..2....2..2..2....2..2..2

Crossrefs

Column 3 of A253004.

Sequence in context: A228284 A248076 A301543 * A229327 A209891 A027006

Adjacent sequences: A252996 A252997 A252998 * A253000 A253001 A253002

Keyword

nonn

Author

R. H. Hardin, Dec 25 2014

Status

approved