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A234559 Number of (n+1) X (3+1) 0..4 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 4 (constant-stress 1 X 1 tilings). 1

%I #6 Jun 20 2022 19:28:51

%S 618,1240,2390,5710,12750,33946,83438,238306,621918,1862530,5040110,

%T 15596050,43132350,136586626,382788878,1232735026,3483571038,

%U 11361560290,32277779630,106316188690,303091761150,1006241261506,2875220234318

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

%H R. H. Hardin, <a href="/A234559/b234559.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) +30*a(n-2) -132*a(n-3) -331*a(n-4) +1720*a(n-5) +1530*a(n-6) -11280*a(n-7) -1324*a(n-8) +39136*a(n-9) -12360*a(n-10) -67968*a(n-11) +39456*a(n-12) +46080*a(n-13) -34560*a(n-14).

%e Some solutions for n=5:

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

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

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

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

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

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

%Y Column 3 of A234564.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 28 2013

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