A253219 Number of n X 4 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.

3, 9, 19, 19, 268, 1249, 3140, 5986, 9792, 14558, 20284, 26970, 34616, 43222, 52788, 63314, 74800, 87246, 100652, 115018, 130344, 146630, 163876, 182082, 201248, 221374, 242460, 264506, 287512, 311478, 336404, 362290, 389136, 416942, 445708

Offset

1,1

Links

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

Formula

Empirical: a(n) = 480*n^2 - 4354*n + 10098 for n>6.

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

G.f.: x*(3 + x^2 - 14*x^3 + 259*x^4 + 483*x^5 + 178*x^6 + 45*x^7 + 5*x^8) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>9.

(End)

Example

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

Crossrefs

Column 4 of A253223.

Sequence in context: A067864 A272513 A270979 * A097267 A043097 A084670

Adjacent sequences: A253216 A253217 A253218 * A253220 A253221 A253222

Keyword

nonn

Author

R. H. Hardin, Dec 29 2014

Status

approved