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A228022
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Irregular triangle read by rows: T(n,k) is the number of binary pattern classes in the (5,n)-rectangular grid with k '1's and (5n-k) '0's: two patterns are in same class if one of them can be obtained by a reflection or 180-degree rotation of the other.
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32
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1, 1, 3, 6, 6, 3, 1, 1, 3, 15, 32, 60, 66, 60, 32, 15, 3, 1, 1, 6, 34, 129, 371, 794, 1310, 1675, 1675, 1310, 794, 371, 129, 34, 6, 1, 1, 6, 56, 294, 1253, 3912, 9808, 19464, 31706, 42116, 46448, 42116, 31706, 19464, 9808, 3912, 1253, 294, 56, 6, 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 5*n+1.
Sum of rows (see example) gives A225829.
Also the number of equivalence classes of ways of placing k 1 X 1 tiles in an n X 5 rectangle under all symmetry operations of the rectangle. - Christopher Hunt Gribble, Apr 24 2015
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LINKS
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EXAMPLE
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Irregular triangle:
1
1 3 6 6 3 1
1 3 15 32 60 66 60 32 15 3 1
1 6 34 129 371 794 1310 1675 1675 1310 794 371 129
34 6 1
1 6 56 294 1253 3912 9808 19464 31706 42116 46448 42116 31706
19464 9808 3912 1253 294 56 6 1
...
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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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