A209724 - OEIS

%I #26 Nov 09 2020 00:36:18

%S 8,9,10,12,14,18,22,30,38,54,70,102,134,198,262,390,518,774,1030,1542,

%T 2054,3078,4102,6150,8198,12294,16390,24582,32774,49158,65542,98310,

%U 131078,196614,262150,393222,524294,786438,1048582,1572870,2097158

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

%C Column 5 of A209727.

%C 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

%H R. H. Hardin, <a href="/A209724/b209724.txt">Table of n, a(n) for n = 1..210</a>

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

%F Conjectures from _Colin Barker_, Mar 07 2018: (Start)

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

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

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

%F (End)

%e Some solutions for n=4:

%e ..2..1..2..1..2..1....2..0..2..0..1..0....2..1..2..1..2..1....0..1..0..1..0..2

%e ..0..2..0..2..0..2....1..2..1..2..0..2....0..2..0..2..0..2....2..0..2..0..2..1

%e ..1..0..1..0..1..0....2..0..2..0..1..0....2..1..2..1..2..1....0..1..0..1..0..2

%e ..0..2..0..2..0..2....1..2..1..2..0..2....0..2..0..2..0..2....2..0..2..0..2..1

%e ..1..0..1..0..1..0....2..0..2..0..1..0....1..0..1..0..1..0....0..1..0..1..0..2

%Y Cf. A153972, A209727.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 12 2012