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

0,3

Comments

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

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

Links

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A336307 A336134 A255214 * A210520 A018144 A115315

Adjacent sequences: A222044 A222045 A222046 * A222048 A222049 A222050

Keyword

nonn

Author

Alois P. Heinz, Feb 06 2013

Status

approved