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A115965
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Number of planar subpartitions of size n pyramidal planar partition.
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0
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OFFSET
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0,2
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COMMENTS
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This is a 2-dimensional analog of the Catalan numbers C_n (A000108). The number of subpartitions of the triangular partition [n,n-1,...,1] is C_{n+1}. The planar partition having its subpartitions counted is:
n n-1 ... 2 1
n-1 n-2 ... 1
... ...
2 1
1
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LINKS
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EXAMPLE
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The 9 planar subpartitions of [2,1|1] are [], [1], [2], [1,1], [1|1], [2,1], [2|1], [1,1|1] and [2,1|1] itself, so a(2)=9. (Here "," separates values on the same line and "|" separates lines.)
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CROSSREFS
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KEYWORD
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more,nonn
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AUTHOR
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STATUS
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approved
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