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Number of (n+1) X (2+1) 0..4 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 19 2022 23:49:29

%S 1120,11574,125080,1377422,15269704,170001402,1894235272,21145362278,

%T 235980939816,2637191479466,29456411908296,329449541332294,

%U 3682458023803816,41215279675356394,460998785806635720

%N Number of (n+1) X (2+1) 0..4 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="/A234445/b234445.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 16*a(n-1) +122*a(n-2) -2854*a(n-3) +3035*a(n-4) +114162*a(n-5) -324660*a(n-6) -1581792*a(n-7) +6105836*a(n-8) +6998392*a(n-9) -41646592*a(n-10) +4188416*a(n-11) +100180352*a(n-12) -55355328*a(n-13) -54337536*a(n-14) +19902720*a(n-15) +7110912*a(n-16) -1815552*a(n-17).

%e Some solutions for n=3:

%e 2 2 2 2 1 4 2 0 4 1 1 1 2 3 4 2 0 2 1 1 0

%e 2 3 4 2 2 4 1 0 3 4 3 2 2 2 2 2 1 2 4 3 1

%e 2 2 2 3 2 3 2 0 2 3 3 3 2 3 4 0 0 0 1 1 0

%e 2 1 0 2 2 2 4 3 4 3 2 1 3 3 3 2 3 2 4 3 1

%Y Column 2 of A234450.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 26 2013