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Number of nX3 0..6 arrays with every 2X2 subblock containing exactly one value repeat, and new values 0..6 introduced in row major order
1

%I #5 Mar 31 2012 12:37:28

%S 5,57,2027,107472,7487423,613535578,54657856108,5063931781244,

%T 477499692659113,45377744955417080,4327164788760402815,

%U 413256848215007047168,39493493565836673722433,3775359326879189119846436

%N Number of nX3 0..6 arrays with every 2X2 subblock containing exactly one value repeat, and new values 0..6 introduced in row major order

%C Column 3 of A209465

%H R. H. Hardin, <a href="/A209460/b209460.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 172*a(n-1) -8737*a(n-2) +125848*a(n-3) +1640003*a(n-4) -58941308*a(n-5) +441046249*a(n-6) +799433456*a(n-7) -23572369886*a(n-8) +84702514904*a(n-9) +67645214404*a(n-10) -904101250144*a(n-11) +1363565491464*a(n-12) +425476260576*a(n-13) -2084864162400*a(n-14) +1100743344000*a(n-15) -104976000000*a(n-16) for n>17

%e Some solutions for n=4

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

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

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

%e ..0..1..2....0..1..0....1..2..0....0..2..2....4..5..1....4..2..4....1..2..1

%K nonn

%O 1,1

%A _R. H. Hardin_ Mar 09 2012