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A228167
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Irregular triangle read by rows: T(n,k) is the number of binary pattern classes in the (8,n)-rectangular grid with k '1's and (8n-k) '0's: two patterns are in the same class if one of them can be obtained by a reflection or 180-degree rotation of the other.
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24
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1, 1, 4, 16, 28, 38, 28, 16, 4, 1, 1, 4, 36, 140, 476, 1092, 2044, 2860, 3270, 2860, 2044, 1092, 476, 140, 36, 4, 1, 1, 8, 84, 536, 2770, 10808, 34116, 87144, 185071, 328208, 492392, 625968, 678524, 625968, 492392, 328208, 185071, 87144, 34116, 10808, 2770, 536, 84, 8, 1
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OFFSET
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0,3
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COMMENTS
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The length of row n is 8*n+1.
Sum of rows (see example) gives A225832.
Also the number of equivalence classes of ways of placing k 1 X 1 tiles in an n X 8 rectangle under all symmetry operations of the rectangle. - Christopher Hunt Gribble, Feb 28 2014
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LINKS
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EXAMPLE
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Irregular triangle:
1
1 4 16 28 38 28 16 4 1
1 4 36 140 476 1092 2044 2860 3270 2860 2044 1092 ...
1 8 84 536 2770 10808 34116 87144 185071 328208 492392 625968 678524 625968 492392 ...
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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