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Number of (n+1) X 5 0..3 arrays with every 2 X 3 or 3 X 2 subblock having exactly three counterclockwise and three clockwise edge increases.
1

%I #7 Dec 11 2015 11:48:33

%S 19660,1269044,83120732,5465582068,359793857820,23692759265020,

%T 1560344155530612,102763262525972772,6767981316129837148,

%U 445739932002608156380,29356499455959182741892,1933423944068169976159444

%N Number of (n+1) X 5 0..3 arrays with every 2 X 3 or 3 X 2 subblock having exactly three counterclockwise and three clockwise edge increases.

%C Column 4 of A206137.

%H R. H. Hardin, <a href="/A206133/b206133.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 116*a(n-1) -4272*a(n-2) +73274*a(n-3) -664822*a(n-4) +3045011*a(n-5) -2689641*a(n-6) -43109752*a(n-7) +221878512*a(n-8) -361728247*a(n-9) -568084610*a(n-10) +3622619867*a(n-11) -6420944192*a(n-12) +2898716070*a(n-13) +7936254065*a(n-14) -16657448946*a(n-15) +14988867773*a(n-16) -6947278317*a(n-17) +1069497024*a(n-18) +493980717*a(n-19) -278060954*a(n-20) +43850387*a(n-21) +2768722*a(n-22) -1728440*a(n-23) +198864*a(n-24) -8316*a(n-25) +108*a(n-26).

%e Some solutions for n=4:

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 04 2012