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Number of (n+1) X (4+1) 0..3 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 2 (constant-stress 1 X 1 tilings).
1

%I #6 Jun 20 2022 19:11:46

%S 3686,13554,49784,183422,677138,2505400,9288710,34509914,128461544,

%T 479146446,1790472578,6703375016,25141441190,94466340970,355552667288,

%U 1340563920974,5062700401010,19151478723096,72561523035974

%N Number of (n+1) X (4+1) 0..3 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 2 (constant-stress 1 X 1 tilings).

%H R. H. Hardin, <a href="/A234486/b234486.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 16*a(n-1) -69*a(n-2) -186*a(n-3) +2233*a(n-4) -3610*a(n-5) -15789*a(n-6) +56088*a(n-7) +1729*a(n-8) -189898*a(n-9) +95019*a(n-10) +304674*a(n-11) -145486*a(n-12) -269396*a(n-13) +58980*a(n-14) +118584*a(n-15) +6480*a(n-16) -16992*a(n-17) -3456*a(n-18).

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 4 of A234490.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 26 2013