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

1,1

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

Links

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

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)

Example

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

Crossrefs

Cf. A153972, A209727.

Sequence in context: A068019 A054011 A280946 * A114842 A169928 A067683

Adjacent sequences: A209721 A209722 A209723 * A209725 A209726 A209727

Keyword

nonn

Author

R. H. Hardin, Mar 12 2012

Status

approved