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1/4 the number of (n+1) X 3 0..3 arrays with every 2 X 2 subblock having one, three or four distinct clockwise edge differences.
1

%I #7 Jun 26 2022 03:36:30

%S 820,42689,2219034,115368738,5997955680,311831135649,16211961522199,

%T 842852674077118,43819535708838103,2278158176293618573,

%U 118440430549650177612,6157665317047215194813,320134281687114509018719

%N 1/4 the number of (n+1) X 3 0..3 arrays with every 2 X 2 subblock having one, three or four distinct clockwise edge differences.

%C Column 2 of A210156.

%H R. H. Hardin, <a href="/A210150/b210150.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 49*a(n-1) +200*a(n-2) -2256*a(n-3) -3750*a(n-4) +29143*a(n-5) -5802*a(n-6) -84658*a(n-7) +57585*a(n-8) +56482*a(n-9) -40584*a(n-10) -14146*a(n-11) +6952*a(n-12) +1280*a(n-13).

%e Some solutions for n=4

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

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

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

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

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

%Y Cf. A210156.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 18 2012