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T(n,k) is the number of (n+1) X (k+1) 0..7 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).
7

%I #6 Jun 20 2022 20:40:55

%S 288,1828,1828,11976,12228,11976,79848,86704,86704,79848,534008,

%T 644188,676192,644188,534008,3577048,4832976,5686836,5686836,4832976,

%U 3577048,23966856,36598068,48272960,55735596,48272960,36598068,23966856

%N T(n,k) is the number of (n+1) X (k+1) 0..7 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).

%C Table starts

%C 288 1828 11976 79848 534008

%C 1828 12228 86704 644188 4832976

%C 11976 86704 676192 5686836 48272960

%C 79848 644188 5686836 55735596 552618120

%C 534008 4832976 48272960 552618120 6369625168

%C 3577048 36598068 417137872 5629225056 76480296484

%C 23966856 278216484 3604917936 57334595276 910186153752

%C 160608008 2124989472 31461207572 593260934340 11128033519340

%C 1076281720 16281513720 274289989296 6129703359580

%C 7212695512 125246817248 2412618175328

%H R. H. Hardin, <a href="/A235078/b235078.txt">Table of n, a(n) for n = 1..84</a>

%F Empirical for column k:

%F k=1: a(n) = 61*a(n-2) -813*a(n-4) +4271*a(n-6) -9694*a(n-8) +8264*a(n-10) -1536*a(n-12).

%F k=2: [order 73].

%e Some solutions for n=2, k=4:

%e 4 7 2 0 4 2 3 2 6 2 6 4 0 4 2 6 4 0 2 0

%e 0 6 4 5 6 0 4 6 7 6 4 5 4 5 0 2 3 2 7 2

%e 4 7 2 6 4 2 3 2 0 2 0 4 0 4 2 4 2 4 6 4

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Jan 03 2014