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A211373
Sum of median parts of all partitions of n into an odd number of parts.
8
0, 1, 2, 4, 5, 9, 12, 18, 24, 37, 47, 68, 89, 123, 160, 218, 276, 370, 472, 615, 778, 1006, 1259, 1607, 2005, 2530, 3136, 3926, 4833, 6004, 7363, 9070, 11067, 13562, 16461, 20053, 24241, 29370, 35362, 42648, 51135, 61400, 73367, 87718, 104448, 124428, 147655
OFFSET
0,3
LINKS
EXAMPLE
a(6) = 12: partitions of 6 into an odd number of parts are [2,1,1,1,1], [2,2,2], [3,2,1], [4,1,1], [6], sum of median parts is 1+2+2+1+6 = 12.
MAPLE
with(combinat):
a:= n-> add(`if`(nops(l)::odd, l[(nops(l)+1)/2], 0), l=partition(n)):
seq(a(n), n=0..40);
MATHEMATICA
a[n_] := Sum[If[OddQ @ Length[l], l[[(Length[l]+1)/2]], 0], {l, IntegerPartitions[n]}];
Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Aug 20 2021, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Feb 06 2013
STATUS
approved