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Number of (n+1) X (2+1) 0..5 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 3, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings).
1

%I #6 Jun 20 2022 00:27:55

%S 332,1200,4312,15572,56276,203768,738516,2680636,9738960,35432228,

%T 129023908,470470536,1717000260,6274522924,22948524144,84039182132,

%U 308005315508,1130228790408,4150565943156,15260094453244,56146361267440

%N Number of (n+1) X (2+1) 0..5 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 3, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings).

%H R. H. Hardin, <a href="/A235020/b235020.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) +40*a(n-2) -213*a(n-3) -616*a(n-4) +3529*a(n-5) +4898*a(n-6) -29657*a(n-7) -24043*a(n-8) +140862*a(n-9) +80302*a(n-10) -394226*a(n-11) -183852*a(n-12) +650340*a(n-13) +268328*a(n-14) -614608*a(n-15) -222048*a(n-16) +318656*a(n-17) +91776*a(n-18) -82432*a(n-19) -14336*a(n-20) +8192*a(n-21).

%e Some solutions for n=4:

%e 0 1 3 4 0 4 4 2 3 4 2 1 0 2 1 5 1 0 3 1 5

%e 1 5 4 3 2 3 5 0 4 2 3 5 4 3 5 3 2 4 1 2 3

%e 0 1 3 4 0 4 4 2 3 4 2 1 5 1 0 1 3 2 2 0 4

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

%e 0 1 3 2 4 2 3 1 2 4 2 1 3 5 4 0 2 1 3 1 5

%Y Column 2 of A235026.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 02 2014