A209724 - OEIS

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

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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