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Search: id:A115965
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| A115965 |
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Number of planar subpartitions of size n pyramidal planar partition. |
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+0
1
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OFFSET
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0,2
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COMMENT
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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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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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Cf. A115728, A115729, A000219, A000108, A008793.
Sequence in context: A011837 A106343 A086992 this_sequence A001142 A111847 A013132
Adjacent sequences: A115962 A115963 A115964 this_sequence A115966 A115967 A115968
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KEYWORD
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more,nonn
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AUTHOR
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Frank Adams-Watters (FrankTAW(AT)Netscape.net), Mar 14 2006
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