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A228169
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Irregular triangle read by rows: T(n,k) is the number of binary pattern classes in the (10,n)-rectangular grid with k '1's and (10n-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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22
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1, 1, 5, 25, 60, 110, 126, 110, 60, 25, 5, 1, 1, 5, 55, 285, 1245, 3876, 9780, 19380, 31650, 41990, 46378, 41990, 31650, 19380, 9780, 3876, 1245, 285, 55, 5, 1, 1, 10, 130, 1070, 7080, 36102, 149785, 511260, 1468215, 3584050, 7523956, 13672690, 21646530, 29964990, 36386895, 38808456, 36386895, 29964990
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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 10*n+1.
Sum of rows (see example) gives A225834.
Also the number of equivalence classes of ways of placing k 1 X 1 tiles in an n X 10 rectangle under all symmetry operations of the rectangle. - Christopher Hunt Gribble, Mar 01 2014
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LINKS
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EXAMPLE
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Irregular triangle:
1
1 5 25 60 110 126 110 60 25 5 1
1 5 55 285 1245 3876 9780 19380 31650 41990 46378 41990...
1 10 130 1070 7080 36102 149785 511260 1468215 3584050 7523956 13672690 21646530 29964990 36386895 38808456 36386895 29964990 21646530 ...
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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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