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A229755
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T(n,k) = number of defective 4-colorings of an n X k 0..3 array connected horizontally, vertically, diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..3 order.
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8
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0, 0, 0, 1, 3, 1, 3, 60, 60, 3, 12, 422, 598, 422, 12, 50, 1840, 2347, 2347, 1840, 50, 210, 6456, 6809, 6561, 6809, 6456, 210, 861, 20032, 17404, 15075, 15075, 17404, 20032, 861, 3416, 57440, 41872, 32548, 29776, 32548, 41872, 57440, 3416, 13140, 155904, 97565, 69198, 57677, 57677, 69198, 97565, 155904, 13140
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OFFSET
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1,5
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COMMENTS
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Table starts
0 0 1 3 12 50 210 861 3416 13140
0 3 60 422 1840 6456 20032 57440 155904 406400
1 60 598 2347 6809 17404 41872 97565 223075 503650
3 422 2347 6561 15075 32548 69198 147376 315786 680124
12 1840 6809 15075 29776 57677 113330 228657 473562 1000381
50 6456 17404 32548 57677 102271 186396 354509 704530 1450667
210 20032 41872 69198 113330 186396 314700 557578 1046550 2070144
861 57440 97565 147376 228657 354509 557578 914039 1594164 2972289
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 12*a(n-1) -57*a(n-2) +136*a(n-3) -171*a(n-4) +108*a(n-5) -27*a(n-6) for n>9
k=2: a(n) = 6*a(n-1) -12*a(n-2) +8*a(n-3) for n>5
k=3: a(n) = 9*a(n-1) -33*a(n-2) +63*a(n-3) -66*a(n-4) +36*a(n-5) -8*a(n-6) for n>8
k=4: a(n) = 9*a(n-1) -33*a(n-2) +63*a(n-3) -66*a(n-4) +36*a(n-5) -8*a(n-6) for n>11
k=5: a(n) = 9*a(n-1) -33*a(n-2) +63*a(n-3) -66*a(n-4) +36*a(n-5) -8*a(n-6) for n>11
k=6: a(n) = 9*a(n-1) -33*a(n-2) +63*a(n-3) -66*a(n-4) +36*a(n-5) -8*a(n-6) for n>11
k=7: a(n) = 9*a(n-1) -33*a(n-2) +63*a(n-3) -66*a(n-4) +36*a(n-5) -8*a(n-6) for n>11
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EXAMPLE
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Some solutions for n=4, k=4:
0 1 2 0 0 1 2 1 0 1 2 1 0 1 2 1 0 1 0 1
0 3 2 3 3 3 0 3 2 3 0 3 3 2 0 3 2 2 3 2
2 1 0 1 2 1 2 2 3 1 2 1 1 2 1 2 3 0 0 1
0 3 2 3 0 3 0 1 2 3 0 3 0 3 0 3 1 2 3 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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