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A235087 T(n,k)=Number of (n+1)X(k+1) 0..4 arrays with every 2X2 subblock having its diagonal sum differing from its antidiagonal sum by 4, with no adjacent elements equal (constant stress tilted 1X1 tilings) 9

%I

%S 38,90,90,202,198,202,478,418,418,478,1078,930,830,930,1078,2554,2002,

%T 1758,1758,2002,2554,5786,4514,3610,3558,3610,4514,5786,13726,9838,

%U 7810,7046,7046,7810,9838,13726,31238,22402,16390,14702,13446,14702,16390

%N T(n,k)=Number of (n+1)X(k+1) 0..4 arrays with every 2X2 subblock having its diagonal sum differing from its antidiagonal sum by 4, with no adjacent elements equal (constant stress tilted 1X1 tilings)

%C Table starts

%C ....38.....90....202....478...1078...2554....5786...13726...31238....74202

%C ....90....198....418....930...2002...4514....9838...22402...49294...113086

%C ...202....418....830...1758...3610...7810...16390...36014...76770...170682

%C ...478....930...1758...3558...7046..14702...29970...63862..132746...287122

%C ..1078...2002...3610...7046..13446..27218...53882..111782..226726...478402

%C ..2554...4514...7810..14702..27218..53590..103702..210318..418838...866298

%C ..5786...9838..16390..29970..53882.103702..196302..390578..764386..1553646

%C .13726..22402..36014..63862.111782.210318..390578..763814.1474106..2953922

%C .31238..49294..76770.132746.226726.418838..764386.1474106.2809478..5563846

%C .74202.113086.170682.287122.478402.866298.1553646.2953922.5563846.10902494

%H R. H. Hardin, <a href="/A235087/b235087.txt">Table of n, a(n) for n = 1..446</a>

%F Empirical for column k (k=4..7 recurrence works for k=1..3 also; apparently all rows and columns satisfy the same order 16 recurrence):

%F k=1: a(n) = 2*a(n-1) +6*a(n-2) -10*a(n-3) -5*a(n-4)

%F k=2: [order 10]

%F k=3: [order 15]

%F k=4..7: [same order 16 recurrence]

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Jan 03 2014

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Last modified June 19 16:01 EDT 2021. Contains 345144 sequences. (Running on oeis4.)