A209724 1/4 the number of (n+1) X 6 0..2 arrays with every 2 X 2 subblock having distinct clockwise edge differences.

8, 9, 10, 12, 14, 18, 22, 30, 38, 54, 70, 102, 134, 198, 262, 390, 518, 774, 1030, 1542, 2054, 3078, 4102, 6150, 8198, 12294, 16390, 24582, 32774, 49158, 65542, 98310, 131078, 196614, 262150, 393222, 524294, 786438, 1048582, 1572870, 2097158

Offset: 1

Author

R. H. Hardin, Mar 12 2012

Keywords

• nonn

Comments

Column 5 of A209727.

Conjecture: a(1) = 8; for n > 1, a(n) is the smallest integer m such that m = ((2x * a(n-1)) /(x+1)) - x , with x a positive nontrivial divisor of m. (This is true at least for a(1) to a(100).) - Enric Reverter i Bigas, Oct 11 2020

Examples

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

Links

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

Crossrefs

Cf. A153972, A209727.

Formula

Empirical: a(n) = a(n-1) +2*a(n-2) -2*a(n-3).

Conjectures from Colin Barker, Mar 07 2018: (Start)

G.f.: x*(8 + x - 15*x^2) / ((1 - x)*(1 - 2*x^2)).

a(n) = 3*2^(n/2-1) + 6 for n even.

a(n) = 2^((n+1)/2) + 6 for n odd.

(End)