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

0,4

Comments

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

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

Links

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

Example

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.

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 *)

Crossrefs

Cf. A006128, A211373, A222044, A222045, A222046, A222047, A222049.

Sequence in context: A156222 A002886 A028724 * A156190 A285446 A367464

Adjacent sequences: A222045 A222046 A222047 * A222049 A222050 A222051

Keyword

nonn

Author

Alois P. Heinz, Feb 06 2013

Status

approved