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Number of (n+1) X (2+1) 0..2 arrays with every 2 X 2 subblock having the absolute values of all six edge and diagonal differences no larger than 1.
1

%I #7 Oct 12 2018 15:32:10

%S 145,1361,12593,116801,1082977,10041953,93113761,863396401,8005833073,

%T 74233997105,688333901137,6382568345057,59182293086657,

%U 548767146042305,5088437180610625,47182476443409233,437498981379983185

%N Number of (n+1) X (2+1) 0..2 arrays with every 2 X 2 subblock having the absolute values of all six edge and diagonal differences no larger than 1.

%H R. H. Hardin, <a href="/A234116/b234116.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 10*a(n-1) - 4*a(n-2) - 26*a(n-3) + 5*a(n-4).

%F Empirical g.f.: x*(145 - 89*x - 437*x^2 + 85*x^3) / (1 - 10*x + 4*x^2 + 26*x^3 - 5*x^4). - _Colin Barker_, Oct 12 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 2 of A234122.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 19 2013