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A235017
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T(n,k) is the number of (n+1) X (k+1) 0..4 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).
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8
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40, 104, 104, 264, 224, 264, 680, 488, 488, 680, 1736, 1112, 936, 1112, 1736, 4456, 2568, 1912, 1912, 2568, 4456, 11400, 6088, 4008, 3560, 4008, 6088, 11400, 29224, 14600, 8760, 6856, 6856, 8760, 14600, 29224, 74824, 35560, 19560, 13912, 12168
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OFFSET
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1,1
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COMMENTS
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Table starts
40 104 264 680 1736 4456 11400 29224 74824 191720
104 224 488 1112 2568 6088 14600 35560 87368 216680
264 488 936 1912 4008 8760 19560 44952 105128 250744
680 1112 1912 3560 6856 13912 28968 62600 138360 314376
1736 2568 4008 6856 12168 23016 44680 90824 189032 407880
4456 6088 8760 13912 23016 40968 74888 144184 283832 581720
11400 14600 19560 28968 44680 74888 128776 235240 437928 853928
29224 35560 44952 62600 90824 144184 235240 410760 729688 1363336
74824 87368 105128 138360 189032 283832 437928 729688 1234216 2211128
191720 216680 250744 314376 407880 581720 853928 1363336 2211128 3822728
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..480
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FORMULA
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Empirical for column k (the k=4..7 recurrence also works for k=1..3; apparently every row and column satisfies the same order 10 recurrence):
k=1: a(n) = a(n-1) +4*a(n-2).
k=2: a(n) = 3*a(n-1) +4*a(n-2) -14*a(n-3) -4*a(n-4) +16*a(n-5).
k=3: [order 8].
k=4..7: [same order 10 recurrence].
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EXAMPLE
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Some solutions for n=4, k=4:
2 1 2 1 2 3 2 0 2 4 3 1 3 1 3 0 4 0 4 0
0 2 0 2 0 1 3 4 3 2 2 3 2 3 2 2 3 2 3 2
2 1 2 1 2 3 2 0 2 4 0 4 0 4 0 4 2 4 2 4
4 0 4 0 4 1 3 4 3 2 2 3 2 3 2 0 1 0 1 0
2 1 2 1 2 3 2 0 2 4 3 1 3 1 3 2 0 2 0 2
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CROSSREFS
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Column 1 is A185761(n+1).
Sequence in context: A235280 A235271 A033832 * A043219 A039396 A043999
Adjacent sequences: A235014 A235015 A235016 * A235018 A235019 A235020
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Jan 02 2014
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STATUS
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approved
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