A253218 Number of n X 3 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.

1, 1, 1, 19, 102, 263, 504, 825, 1226, 1707, 2268, 2909, 3630, 4431, 5312, 6273, 7314, 8435, 9636, 10917, 12278, 13719, 15240, 16841, 18522, 20283, 22124, 24045, 26046, 28127, 30288, 32529, 34850, 37251, 39732, 42293, 44934, 47655, 50456, 53337, 56298

Offset

1,4

Links

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

Formula

Empirical: a(n) = 40*n^2 - 279*n + 497 for n>4.

Conjectures from Colin Barker, Dec 09 2018: (Start)

G.f.: x*(1 - 2*x + x^2 + 18*x^3 + 47*x^4 + 13*x^5 + 2*x^6) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>7.

(End)

Example

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

Crossrefs

Column 3 of A253223.

Sequence in context: A061696 A062643 A245528 * A300774 A054658 A023296

Adjacent sequences: A253215 A253216 A253217 * A253219 A253220 A253221

Keyword

nonn

Author

R. H. Hardin, Dec 29 2014

Status

approved