A253220 Number of n X 5 nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 2 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.

6, 25, 102, 268, 268, 3568, 16028, 40238, 77063, 126673, 189083, 264293, 352303, 453113, 566723, 693133, 832343, 984353, 1149163, 1326773, 1517183, 1720393, 1936403, 2165213, 2406823, 2661233, 2928443, 3208453, 3501263, 3806873, 4125283

Offset

1,1

Links

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

Formula

Empirical: a(n) = 6400*n^2 - 71990*n + 206573 for n>8.

Conjectures from Colin Barker, Dec 10 2018: (Start)

G.f.: x*(6 + 7*x + 45*x^2 + 31*x^3 - 255*x^4 + 3466*x^5 + 5860*x^6 + 2590*x^7 + 865*x^8 + 170*x^9 + 15*x^10) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>11.

(End)

Example

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

Crossrefs

Column 5 of A253223.

Sequence in context: A346390 A323824 A037537 * A037481 A199844 A267536

Adjacent sequences: A253217 A253218 A253219 * A253221 A253222 A253223

Keyword

nonn

Author

R. H. Hardin, Dec 29 2014

Status

approved