Search: a036054 -id:a036054
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A036045
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Sum of distances between dual pairs of partitions of n for the canonical order.
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+10
11
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0, 2, 4, 12, 24, 60, 110, 238, 436, 860, 1516, 2848, 4874, 8666, 14664, 25120, 41342, 69178, 111596, 181890, 289170, 461086, 720944, 1131358, 1743016, 2689332, 4094090, 6228298, 9364440, 14072828, 20926402, 31080270, 45767490, 67255096, 98095260, 142805322
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OFFSET
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1,2
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COMMENTS
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Canonical order means each partition is sorted in descending order of part size and then the partitions are listed in lexicographic order.
a(n) is even since for parts that are not self-dual the distance between a part and its dual is counted twice, and for parts that are self-dual the distance is zero. (End)
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LINKS
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EXAMPLE
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a(4) = 12 = sum of {1,5},{2,4},{3,3},{4,2},{5,1} = 4 + 2 + 0 + 2 + 4.
Case n = 4: The partitions of 4 in canonical order are:
1) [1,1,1,1]
2) [2,1,1]
3) [2,2]
4) [3,1]
5) [4]
Partitions [1,1,1,1] and [4] are dual, partitions [2,1,1] and [3,1] are dual and partition [2,2] is self-dual.
Summing the distance between each element and its dual gives:
a(4) = |1-5| + |2-4| + |3-3| + |4-2| + |5-1| = 12.
(End)
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CROSSREFS
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Cf. A036046, A036047, A036048, A036049, A036050, A036051, A036052, A036053, A036054, A036055, A036056.
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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