A253007 Number of n X 4 nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 3 and every value increasing by 0 or 1 with every step right, diagonally se or down.

1, 1, 1, 1, 124, 3423, 33533, 158877, 490403, 1156178, 2286874, 4013538, 6467242, 9779058, 14080058, 19501314, 26173898, 34228882, 43797338, 55010338, 67998954, 82894258, 99827322, 118929218, 140331018, 164163794, 190558618, 219646562

Offset: 1

Author

R. H. Hardin, Dec 25 2014

Keywords

• nonn

Examples

			Some solutions for n=6:
..0..0..1..1....0..0..0..0....0..0..0..0....0..1..1..2....0..0..0..1
..0..0..1..1....0..1..1..1....1..1..1..1....0..1..1..2....0..0..0..1
..1..1..1..1....1..1..2..2....1..1..2..2....0..1..1..2....0..0..1..1
..2..2..2..2....1..1..2..2....1..2..2..2....1..1..1..2....0..0..1..2
..2..2..2..2....1..1..2..2....1..2..2..2....1..1..1..2....0..1..1..2
..2..2..2..2....1..1..2..2....1..2..2..2....1..1..1..2....1..1..2..2
		

Links

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

Crossrefs

Column 4 of A253011.

Formula

Empirical: a(n) = (65536/3)*n^3 - 422912*n^2 + (8343128/3)*n - 6208382 for n>9.

Conjectures from Colin Barker, Dec 08 2018: (Start)

G.f.: x*(1 - 3*x + 3*x^2 - x^3 + 123*x^4 + 2930*x^5 + 20582*x^6 + 44788*x^7 + 42525*x^8 + 17119*x^9 + 2605*x^10 + 375*x^11 + 25*x^12) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>13.

(End)