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A235186
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T(n,k) is the number of (n+1) X (k+1) 0..5 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 5, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings).
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9
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72, 212, 212, 576, 560, 576, 1696, 1400, 1400, 1696, 4656, 3796, 3240, 3796, 4656, 13736, 9780, 8224, 8224, 9780, 13736, 38064, 27080, 19952, 19584, 19952, 27080, 38064, 112504, 71244, 52328, 45128, 45128, 52328, 71244, 112504, 314448, 200164
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OFFSET
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1,1
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LINKS
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FORMULA
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Empirical for column k (the k=4..7 recurrence works also for k=1..3; apparently all rows and columns satisfy the same order 27 recurrence):
k=1: a(n) = 16*a(n-2) -65*a(n-4) +14*a(n-6).
k=2: [order 18].
k=3: [order 26].
k=4..7: [same order 27 recurrence].
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EXAMPLE
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Table starts
72 212 576 1696 4656 13736 38064 112504 314448
212 560 1400 3796 9780 27080 71244 200164 535384
576 1400 3240 8224 19952 52328 131120 352000 903544
1696 3796 8224 19584 45128 112432 270056 694680 1719360
4656 9780 19952 45128 99096 236376 545768 1351904 3234336
13736 27080 52328 112432 236376 540368 1204056 2877232 6679048
38064 71244 131120 270056 545768 1204056 2598040 6019088 13595968
112504 200164 352000 694680 1351904 2877232 6019088 13521264 29758464
314448 535384 903544 1719360 3234336 6679048 13595968 29758464 64019304
930968 1520236 2468016 4527576 8236464 16488928 32649376 69567168 146227600
Some solutions for n=4, k=4:
4 1 3 1 3 1 3 1 4 2 5 3 5 3 4 0 3 1 5 2
1 3 0 3 0 4 1 4 2 5 1 4 1 4 0 3 1 4 3 5
5 2 4 2 4 2 4 2 5 3 3 1 3 1 2 0 3 1 5 2
2 4 1 4 1 4 1 4 2 5 1 4 1 4 0 3 1 4 3 5
5 2 4 2 4 2 4 2 5 3 2 0 2 0 1 0 3 1 5 2
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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