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A211373
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Sum of median parts of all partitions of n into an odd number of parts.
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8
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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
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OFFSET
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0,3
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LINKS
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EXAMPLE
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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.
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MAPLE
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with(combinat):
a:= n-> add(`if`(nops(l)::odd, l[(nops(l)+1)/2], 0), l=partition(n)):
seq(a(n), n=0..40);
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MATHEMATICA
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a[n_] := Sum[If[OddQ @ Length[l], l[[(Length[l]+1)/2]], 0], {l, IntegerPartitions[n]}];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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