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

0,3

Links

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

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

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

Sequence in context: A241339 A327781 A241411 * A241734 A371171 A039898

Adjacent sequences: A211370 A211371 A211372 * A211374 A211375 A211376

Keyword

nonn

Author

Alois P. Heinz, Feb 06 2013

Status

approved