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Number of (n+1) X (1+1) 0..5 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 #13 Jun 20 2022 21:32:26

%S 280,2400,21344,192960,1755520,16026240,146415104,1339023360,

%T 12242606080,111999882240,1024150052864,9369857679360,85682076221440,

%U 783906124554240,7168413301735424,65584009257615360,599732112759193600

%N Number of (n+1) X (1+1) 0..5 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="/A234452/b234452.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 100*a(n-2) - 1384*a(n-4) + 1440*a(n-6).

%F Empirical g.f.: 8*x*(35 + 300*x - 832*x^2 - 5880*x^3 + 1080*x^4 + 6480*x^5) / (1 - 100*x^2 + 1384*x^4 - 1440*x^6). - _Colin Barker_, Oct 15 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 1 of A234458.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 26 2013