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 A036045 Sum of distances between dual pairs of partitions of n for the canonical order. 11
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS From Andrew Howroyd, Sep 16 2019: (Start) 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) LINKS EXAMPLE a(4) = 12 = sum of {1,5},{2,4},{3,3},{4,2},{5,1} = 4 + 2 + 0 + 2 + 4. From Andrew Howroyd, Sep 16 2019: (Start) 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) CROSSREFS Cf. A036046, A036047, A036048, A036049, A036050, A036051, A036052, A036053, A036054, A036055, A036056. Sequence in context: A045687 A233411 A057422 * A331392 A100538 A303794 Adjacent sequences:  A036042 A036043 A036044 * A036046 A036047 A036048 KEYWORD nonn,nice AUTHOR EXTENSIONS a(31)-a(36) from Andrew Howroyd, Sep 16 2019 STATUS approved

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Last modified March 31 19:37 EDT 2020. Contains 333151 sequences. (Running on oeis4.)