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A234779 Number of (n+1) X (1+1) 0..3 arrays with no adjacent elements equal and with each 2 X 2 subblock having the number of clockwise edge increases equal to the number of counterclockwise edge increases. 1

%I #8 Oct 16 2018 05:42:03

%S 76,484,3084,19652,125228,797988,5085004,32403076,206481516,

%T 1315758308,8384382092,53427641412,340455961516,2169481164964,

%U 13824544308684,88093885500932,561359021271788,3577137606898788,22794527163204364

%N Number of (n+1) X (1+1) 0..3 arrays with no adjacent elements equal and with each 2 X 2 subblock having the number of clockwise edge increases equal to the number of counterclockwise edge increases.

%H R. H. Hardin, <a href="/A234779/b234779.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 7*a(n-1) - 4*a(n-2).

%F Conjectures from _Colin Barker_, Oct 16 2018: (Start)

%F G.f.: 4*x*(19 - 12*x) / (1 - 7*x + 4*x^2).

%F a(n) = (2^(1-n)*((7-sqrt(33))^n*(-17+3*sqrt(33)) + (7+sqrt(33))^n*(17+3*sqrt(33)))) / sqrt(33).

%F (End)

%e Some solutions for n=5:

%e ..3..2....2..0....1..0....2..3....3..2....3..2....1..0....1..2....2..0....2..1

%e ..2..1....0..3....0..1....1..2....2..1....2..1....2..1....2..0....1..3....0..2

%e ..0..2....2..1....2..3....3..0....1..3....0..3....0..3....1..3....3..1....1..3

%e ..2..0....1..3....0..1....2..3....2..0....3..0....3..2....2..0....1..3....0..1

%e ..0..3....0..1....2..3....0..1....0..1....0..2....0..3....3..2....0..1....1..3

%e ..3..0....3..0....3..2....1..0....3..0....1..3....3..0....2..1....1..3....2..1

%Y Column 1 of A234786.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 30 2013

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Last modified April 16 05:35 EDT 2024. Contains 371697 sequences. (Running on oeis4.)