A252834 Number of n X 6 nonnegative integer arrays with upper left 0 and every value within 2 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.

16, 85, 529, 3365, 18528, 78674, 244131, 569420, 1070036, 1750150, 2610438, 3650950, 4871686, 6272646, 7853830, 9615238, 11556870, 13678726, 15980806, 18463110, 21125638, 23968390, 26991366, 30194566, 33577990, 37141638, 40885510

Offset

1,1

Links

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

Formula

Empirical: a(n) = 90112*n^2 - 1032064*n + 3059590 for n>9.

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

G.f.: x*(16 + 37*x + 322*x^2 + 2017*x^3 + 9935*x^4 + 32656*x^5 + 60328*x^6 + 54521*x^7 + 15495*x^8 + 4171*x^9 + 676*x^10 + 50*x^11) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>12.

(End)

Example

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

Crossrefs

Column 6 of A252836.

Sequence in context: A231941 A118675 A223962 * A050256 A223835 A224143

Adjacent sequences: A252831 A252832 A252833 * A252835 A252836 A252837

Keyword

nonn

Author

R. H. Hardin, Dec 22 2014

Status

approved