A208253 Number of n X 3 0..2 arrays with new values 0..2 introduced in row major order and no element equal to more than one of its immediate leftward or upward neighbors.

5, 96, 2040, 43344, 920928, 19566912, 415737216, 8833148160, 187677464064, 3987573838848, 84723785029632, 1800122089230336, 38247105402593280, 812634365429366784, 17266002353004576768, 366849901919230820352

Offset: 1

Author

R. H. Hardin, Feb 24 2012

Keywords

• nonn

Comments

Column 3 of A208258.

Examples

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

Links

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

Crossrefs

Cf. A208258.

Formula

Empirical: a(n) = 22*a(n-1) - 16*a(n-2) for n>3.

Conjectures from Colin Barker, Jun 29 2018: (Start)

G.f.: x*(1 - 2*x)*(5 - 4*x) / (1 - 22*x + 16*x^2).

a(n) = (1/32)*sqrt(3/35)*((11-sqrt(105))^n*(-13+sqrt(105)) + (11+sqrt(105))^n*(13+sqrt(105))) for n>1.

(End)