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A228168
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Irregular triangle read by rows: T(n,k) is the number of binary pattern classes in the (9,n)-rectangular grid with k '1's and (9n-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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23
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1, 1, 5, 20, 44, 66, 66, 44, 20, 5, 1, 1, 5, 45, 208, 792, 2156, 4704, 7984, 11034, 12190, 11034, 7984, 4704, 2156, 792, 208, 45, 5, 1, 1, 10, 106, 785, 4554, 20556, 74828, 223498, 557599, 1175574, 2114550, 3266415, 4354188, 5023464, 5023464, 4354188
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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 9*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 9 rectangle under all symmetry operations of the rectangle. - Christopher Hunt Gribble, Apr 27 2015
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LINKS
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EXAMPLE
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Irregular triangle:
1
1 5 20 44 66 66 44 20 5 1
1 5 45 208 792 2156 4704 7984 11034 12190 11034 7984 ...
1 10 106 785 4554 20556 74828 223498 557599 1175574 2114550 3266415 4354188 5023464 5023464 4354188 3266415 2114550 1175574 ...
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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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