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A183672
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T(n,k)=Number of (n+1)X(k+1) 0..6 arrays with every 2X2 subblock summing to 12
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10
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231, 1225, 1225, 6951, 5215, 6951, 41209, 24745, 24745, 41209, 251991, 126223, 100935, 126223, 251991, 1577065, 678265, 451801, 451801, 678265, 1577065, 10049991, 3791935, 2163831, 1803007, 2163831, 3791935, 10049991, 64979929
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OFFSET
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1,1
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COMMENTS
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Table starts
........231......1225......6951.....41209....251991...1577065..10049991
.......1225......5215.....24745....126223....678265...3791935..21874825
.......6951.....24745....100935....451801...2163831..10914505..57370215
......41209....126223....451801...1803007...7794409..35840623.173139001
.....251991....678265...2163831...7794409..30722151.129866905.580718871
....1577065...3791935..10914505..35840623.129866905
...10049991..21874825..57370215.173139001
...64979929.129463663.311907001
..425156151.782782105
.2809324105
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LINKS
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FORMULA
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Empirical, for every row and column: a(n)=28*a(n-1)-322*a(n-2)+1960*a(n-3)-6769*a(n-4)+13132*a(n-5)-13068*a(n-6)+5040*a(n-7)
The coefficient of a(n-i) is -s(8,8-i), s() being the Stirling number of the first kind, via D. S. McNeil and M. F. Hasler in the Sequence Fans Mailing List.
For a 0..z array with 2X2 blocks summing to 2z, the coefficients are -s(z+2,z+2-i)
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EXAMPLE
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Some solutions for 4X3
..4..1..5....5..2..5....2..2..1....6..2..4....3..1..5....5..1..5....0..6..1
..6..1..5....2..3..2....3..5..4....2..2..4....3..5..1....6..0..6....3..3..2
..3..2..4....4..3..4....4..0..3....4..4..2....4..0..6....3..3..3....0..6..1
..5..2..4....1..4..1....2..6..3....3..1..5....6..2..4....1..5..1....3..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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