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

%I #6 Jun 20 2022 18:19:44

%S 448,2804,17200,108404,666880,4221580,26023136,165444308,1021780992,

%T 6523295060,40358959904,258707287924,1603224318880,10317081808148,

%U 64032676563232,413605116397892,2570619151590496,16663502963008084

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

%H R. H. Hardin, <a href="/A234438/b234438.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 119*a(n-2) -4884*a(n-4) +76112*a(n-6) -295366*a(n-8) +424128*a(n-10) -242512*a(n-12) +58736*a(n-14) -4992*a(n-16).

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 3 of A234443.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 26 2013