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T(n,k)=Number is the number of (n+1) X (k+1) 0..6 arrays with every 2X2 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 3, with no adjacent elements equal (constant -stress tilted 1X1 1 X 1 tilings).

....... 168........ 848........ 4352........ 22576........ 117232........ 609412

....... 848....... 4348....... 22936....... 125196........ 685028....... 3780180

...... 4352...... 22936...... 126040....... 727376....... 4212792...... 24652260

..... 22576..... 125196...... 727376...... 4548100...... 28470232..... 181669172

.... 117232..... 685028..... 4212792..... 28470232..... 192475088.... 1333866324

.... 609412.... 3780180.... 24652260.... 181669172.... 1333866324... 10169860740

... 3167392... 20896656... 144439680... 1158928396.... 9228249720... 77175918060

.. 16467664.. 116103776... 851021376... 7478244692... 64770384460.. 600121202116

.. 85596352.. 646515740.. 5022415256.. 48319836696.. 454460234224. 4656911119264

. 445030452. 3615891056. 29788907152. 315434737336. 3229635581416

k=1: a(n) = 35*a(n-2) -235*a(n-4) +543*a(n-6) -458*a(n-8) +96*a(n-10).

k=2: [order 40].

Some solutions for n=3 , k=4:

.. 0.. 2.. 1.. 5.. 3.... 3.. 5.. 4.. 5.. 6.... 0.. 2.. 4.. 6.. 4.... 0.. 1.. 0.. 4.. 3

.. 4.. 3.. 5.. 6.. 1.... 4.. 3.. 5.. 3.. 1.... 1.. 6.. 5.. 4.. 5.... 1.. 5.. 1.. 2.. 4

.. 3.. 5.. 4.. 2.. 0.... 5.. 1.. 0.. 1.. 2.... 0.. 2.. 4.. 6.. 4.... 0.. 1.. 0.. 4.. 3

.. 2.. 1.. 3.. 4.. 5.... 6.. 5.. 1.. 5.. 3.... 2.. 1.. 6.. 5.. 0.... 2.. 0.. 2.. 3.. 5

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R. H. Hardin, <a href="/A235071/b235071.txt">Table of n, a(n) for n = 1..112</a>

allocated for R. H. Hardin

T(n,k)=Number of (n+1)X(k+1) 0..6 arrays with every 2X2 subblock having its diagonal sum differing from its antidiagonal sum by 3, with no adjacent elements equal (constant stress tilted 1X1 tilings)

168, 848, 848, 4352, 4348, 4352, 22576, 22936, 22936, 22576, 117232, 125196, 126040, 125196, 117232, 609412, 685028, 727376, 727376, 685028, 609412, 3167392, 3780180, 4212792, 4548100, 4212792, 3780180, 3167392, 16467664, 20896656, 24652260

1,1

Table starts

.......168........848........4352........22576........117232........609412

.......848.......4348.......22936.......125196........685028.......3780180

......4352......22936......126040.......727376.......4212792......24652260

.....22576.....125196......727376......4548100......28470232.....181669172

....117232.....685028.....4212792.....28470232.....192475088....1333866324

....609412....3780180....24652260....181669172....1333866324...10169860740

...3167392...20896656...144439680...1158928396....9228249720...77175918060

..16467664..116103776...851021376...7478244692...64770384460..600121202116

..85596352..646515740..5022415256..48319836696..454460234224.4656911119264

.445030452.3615891056.29788907152.315434737336.3229635581416

Empirical for column k:

k=1: a(n) = 35*a(n-2) -235*a(n-4) +543*a(n-6) -458*a(n-8) +96*a(n-10)

k=2: [order 40]

Some solutions for n=3 k=4

..0..2..1..5..3....3..5..4..5..6....0..2..4..6..4....0..1..0..4..3

..4..3..5..6..1....4..3..5..3..1....1..6..5..4..5....1..5..1..2..4

..3..5..4..2..0....5..1..0..1..2....0..2..4..6..4....0..1..0..4..3

..2..1..3..4..5....6..5..1..5..3....2..1..6..5..0....2..0..2..3..5

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nonn,tabl

R. H. Hardin, Jan 03 2014

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