A252831 Number of n X 3 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.

4, 13, 44, 127, 288, 529, 850, 1251, 1732, 2293, 2934, 3655, 4456, 5337, 6298, 7339, 8460, 9661, 10942, 12303, 13744, 15265, 16866, 18547, 20308, 22149, 24070, 26071, 28152, 30313, 32554, 34875, 37276, 39757, 42318, 44959, 47680, 50481, 53362, 56323

Offset: 1

Author

R. H. Hardin, Dec 22 2014

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Column 3 of A252836.

Formula

Empirical: a(n) = 40*n^2 - 199*n + 283 for n>3.

Conjectures from Colin Barker, Dec 06 2018: (Start)

G.f.: x*(4 + x + 17*x^2 + 30*x^3 + 26*x^4 + 2*x^5) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>6.

(End)