%I
%S 0,2,4,12,24,60,110,238,436,860,1516,2848,4874,8666,14664,25120,41342,
%T 69178,111596,181890,289170,461086,720944,1131358,1743016,2689332,
%U 4094090,6228298,9364440,14072828,20926402,31080270,45767490,67255096,98095260,142805322
%N Sum of distances between dual pairs of partitions of n for the canonical order.
%C From _Andrew Howroyd_, Sep 16 2019: (Start)
%C Canonical order means each partition is sorted in descending order of part size and then the partitions are listed in lexicographic order.
%C a(n) is even since for parts that are not selfdual the distance between a part and its dual is counted twice, and for parts that are selfdual the distance is zero. (End)
%e a(4) = 12 = sum of {1,5},{2,4},{3,3},{4,2},{5,1} = 4 + 2 + 0 + 2 + 4.
%e From _Andrew Howroyd_, Sep 16 2019: (Start)
%e Case n = 4: The partitions of 4 in canonical order are:
%e 1) [1,1,1,1]
%e 2) [2,1,1]
%e 3) [2,2]
%e 4) [3,1]
%e 5) [4]
%e Partitions [1,1,1,1] and [4] are dual, partitions [2,1,1] and [3,1] are dual and partition [2,2] is selfdual.
%e Summing the distance between each element and its dual gives:
%e a(4) = 15 + 24 + 33 + 42 + 51 = 12.
%e (End)
%Y Cf. A036046, A036047, A036048, A036049, A036050, A036051, A036052, A036053, A036054, A036055, A036056.
%K nonn,nice
%O 1,2
%A _Olivier GĂ©rard_
%E a(31)a(36) from _Andrew Howroyd_, Sep 16 2019
