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Number of (n+1)X(2+1) 0..2 arrays with the upper median plus the lower median of every 2X2 subblock differing from its horizontal and vertical neighbors by exactly one
1

%I #4 Feb 09 2014 06:55:05

%S 316,1536,7356,36168,175768,848720,4121060,20050460,97225972,

%T 471641072,2290359200,11118632740,53953373220,261887194692,

%U 1271260706180,6170274480252,29948363314372,145366959304036,705586332210288

%N Number of (n+1)X(2+1) 0..2 arrays with the upper median plus the lower median of every 2X2 subblock differing from its horizontal and vertical neighbors by exactly one

%C Column 2 of A237567

%H R. H. Hardin, <a href="/A237561/b237561.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-2) +42*a(n-3) +208*a(n-4) +293*a(n-5) +900*a(n-6) -12*a(n-7) -857*a(n-8) -1583*a(n-9) -4726*a(n-10) +4946*a(n-11) +5993*a(n-12) +3312*a(n-13) +3822*a(n-14) -3319*a(n-15) -540*a(n-16) -32*a(n-17)

%e Some solutions for n=5

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

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 09 2014