A222047 Sum of largest parts of all partitions of n into an odd number of parts.

0, 1, 2, 4, 6, 11, 17, 28, 41, 66, 93, 140, 195, 282, 384, 541, 722, 992, 1311, 1762, 2299, 3045, 3929, 5127, 6559, 8458, 10726, 13689, 17225, 21780, 27224, 34134, 42387, 52769, 65138, 80544, 98887, 121538, 148456, 181456, 220590, 268252, 324677, 392961

Offset: 0

Author

Alois P. Heinz, Feb 06 2013

Keywords

• nonn

Comments

a(n) + A222048(n) = A006128(n).

a(n) - A222048(n) = A222049(n).

Examples

			a(6) = 17: 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 largest parts is 2+2+3+4+6 = 17.
		

Links

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

Crossrefs

Cf. A006128, A211373, A222044, A222045, A222046, A222048, A222049.

Programs

Maple

b:= proc(n, i) option remember; [`if`(n=i, n, 0), 0]+
      `if`(i>n, [0, 0], b(n, i+1)+(l-> [l[2], l[1]])(b(n-i, i)))
    end:
a:= n-> b(n,1)[1]:
seq(a(n), n=0..50);

Mathematica

Table[Total[Max[#]&/@Select[IntegerPartitions[n],OddQ[Length[#]]&]],{n,0,50}] (* Harvey P. Dale, Apr 19 2014 *)
b[n_, i_] := b[n, i] = {If[n==i, n, 0], 0} + If[i>n, {0, 0}, b[n, i+1] + Reverse[b[n-i, i]]]; a[n_] := b[n, 1][[1]]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Aug 30 2016, after Alois P. Heinz *)