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A234678 Number of (n+1) X (5+1) 0..5 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 5 (constant-stress 1 X 1 tilings). 1

%I #6 Jun 20 2022 19:47:09

%S 14368,25292,43240,93680,191128,476648,1109272,3039128,7775608,

%T 22805432,62414680,192810680,553489528,1779951608,5286609112,

%U 17539418168,53391783928,181456023032,562412044120,1947069844280,6115700862328

%N Number of (n+1) X (5+1) 0..5 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 5 (constant-stress 1 X 1 tilings).

%H R. H. Hardin, <a href="/A234678/b234678.txt">Table of n, a(n) for n = 1..163</a>

%F Empirical: a(n) = 4*a(n-1) +47*a(n-2) -200*a(n-3) -901*a(n-4) +4204*a(n-5) +8957*a(n-6) -48440*a(n-7) -47194*a(n-8) +334096*a(n-9) +101948*a(n-10) -1410080*a(n-11) +170136*a(n-12) +3549696*a(n-13) -1446912*a(n-14) -4861440*a(n-15) +2954880*a(n-16) +2764800*a(n-17) -2073600*a(n-18).

%e Some solutions for n=5:

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

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

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

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

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

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

%Y Column 5 of A234681.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 29 2013

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