A211373 Sum of median parts of all partitions of n into an odd number of parts.

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

Author

Alois P. Heinz, Feb 06 2013

Keywords

• nonn

Examples

			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.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A222044, A222045, A222047, A222048, A268359.

Programs

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 *)