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A185761 Number of (n+1) X 2 binary arrays with no 2 X 2 subblock trace equal to any horizontal or vertical neighbor 2 X 2 subblock trace. 3

%I #8 Feb 22 2018 09:13:55

%S 16,40,104,264,680,1736,4456,11400,29224,74824,191720,491016,1257896,

%T 3221960,8253544,21141384,54155560,138721096,355343336,910227720,

%U 2331601064,5972511944,15298916200,39188963976,100384628776,257140484680

%N Number of (n+1) X 2 binary arrays with no 2 X 2 subblock trace equal to any horizontal or vertical neighbor 2 X 2 subblock trace.

%C Column 1 of A185769.

%H R. H. Hardin, <a href="/A185761/b185761.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = a(n-1) + 4*a(n-2).

%F Conjectures from _Colin Barker_, Feb 22 2018: (Start)

%F G.f.: 8*x*(2 + 3*x) / (1 - x - 4*x^2).

%F a(n) = (2^(-n)*((1-sqrt(17))^n*(-13+3*sqrt(17)) + (1+sqrt(17))^n*(13+3*sqrt(17)))) / sqrt(17).

%F (End)

%e Some solutions for 3 X 2:

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

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

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

%Y Cf. A185769.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 03 2011

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)