A252980 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 increasing by 0 or 1 with every step right, diagonally se or down.

6, 41, 266, 1247, 4657, 67537, 433401, 1481460, 3510600, 6637020, 10878576, 16235268, 22707096, 30294060, 38996160, 48813396, 59745768, 71793276, 84955920, 99233700, 114626616, 131134668, 148757856, 167496180, 187349640, 208318236

Offset: 1

Author

R. H. Hardin, Dec 25 2014

Keywords

• nonn

Comments

Column 5 of A252983.

Examples

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

Links

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

Crossrefs

Cf. A252983.

Formula

Empirical: a(n) = 557568*n^2 - 7467372*n + 25553940 for n>8.

Conjectures from Colin Barker, Mar 20 2018: (Start)

G.f.: x*(6 + 23*x + 161*x^2 + 566*x^3 + 1673*x^4 + 57041*x^5 + 243514*x^6 + 379211*x^7 + 298886*x^8 + 116199*x^9 + 17856*x^10) / (1 - x)^3.

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

(End)