A222048 Sum of largest parts of all partitions of n into an even number of parts.

0, 0, 1, 2, 6, 9, 18, 26, 45, 62, 99, 135, 204, 274, 396, 527, 741, 973, 1333, 1736, 2331, 3007, 3970, 5079, 6615, 8393, 10796, 13605, 17320, 21673, 27339, 34001, 42540, 52597, 65324, 80332, 99127, 121274, 148745, 181131, 220956, 267852, 325114, 392476, 474178

Offset: 0

Author

Alois P. Heinz, Feb 06 2013

Keywords

• nonn

Comments

A222047(n) + a(n) = A006128(n).

A222047(n) - a(n) = A222049(n).

Examples

			a(6) = 18: partitions of 6 into an even number of parts are [1,1,1,1,1,1], [2,2,1,1], [3,1,1,1], [3,3], [4,2], [5,1], sum of largest parts is 1+2+3+3+4+5 = 18.
		

Links

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

Crossrefs

Cf. A006128, A211373, A222044, A222045, A222046, A222047, 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)[2]:
seq(a(n), n=0..50);

Mathematica

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][[2]]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Feb 02 2017, translated from Maple *)