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Search: id:A145574
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| A145574 |
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Array a(n,m) for number of partitions of n>=2 with m parts having no part 1. Hence m=1..floor(n/2). |
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2
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| 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 3, 3, 1, 1, 4, 4, 2, 1, 1, 4, 5, 3, 1, 1, 5, 7, 5, 2, 1, 1, 5, 8, 6, 3, 1, 1, 6, 10, 9, 5, 2, 1, 1, 6, 12, 11, 7, 3, 1, 1, 7, 14, 15, 10, 5, 2, 1, 1, 7, 16, 18, 13, 7, 3, 1, 1, 8, 19, 23, 18, 11, 5, 2, 1, 1, 8, 21, 27, 23, 14, 7, 3, 1, 1, 9, 24, 34, 30
(list; graph; listen)
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OFFSET
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2,8
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COMMENT
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The row lengths sequence is floor(n/2) = [1,1,2,2,3,3,4,4,...], see A008619(n-1), n>=2.
Obtained from the characteristic partition array A145573 by summing in row n>=2 over entries belonging to like parts number m.
The column sequences give A000012, A004526, A001399, A001400, A001401, A001402, A026813 for m=1..7.
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LINKS
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W. Lang, M. Sjodahl First 20 rows of the array and row sums.
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FORMULA
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a(n,m)=sum over entries of A145573(n,k) array which belong to partitions with part number m, for m=1..floor(n/2)). Note that partitions with parts number m>floor(n/2) have always at least one part 1.
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EXAMPLE
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[1];[1];[1,1];[1,1];[1,2,1];[1,2,1];[1,3,2,1];[1,3,3,1];[1,4,4,2,1],...
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CROSSREFS
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Cf. A145573, A002865 (row sums).
Sequence in context: A078770 A072038 A108316 this_sequence A056138 A067594 A089533
Adjacent sequences: A145571 A145572 A145573 this_sequence A145575 A145576 A145577
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KEYWORD
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nonn,easy,tabf
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) and Malin Sjodahl (malin.sjodahl(AT)physik.uni-karlsruhe.de) Mar 06 2009
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