A222044 Sum of smallest parts of all partitions of n into an odd number of parts.

0, 1, 2, 4, 5, 8, 11, 15, 19, 28, 35, 47, 61, 80, 102, 136, 168, 218, 276, 350, 437, 556, 686, 860, 1063, 1321, 1620, 2005, 2443, 2998, 3649, 4445, 5377, 6531, 7863, 9496, 11398, 13694, 16373, 19603, 23347, 27834, 33058, 39259, 46467, 55020, 64914, 76599

Offset

0,3

Comments

a(n) + A222045(n) = A046746(n).

a(n) - A222045(n) = A222046(n).

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Alois P. Heinz)

Formula

a(n) ~ exp(Pi*sqrt(2*n/3)) / (8*sqrt(3)*n). - Vaclav Kotesovec, Jul 06 2019

Example

a(6) = 11: 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 smallest parts is 1+2+1+1+6 = 11.

Maple

b:= proc(n, i) option remember;
      [`if`(n=i, n, 0), 0]+`if`(i<1, [0, 0], b(n, i-1)+
       `if`(n<i, [0, 0], (l-> [l[2], l[1]])(b(n-i, i))))
    end:
a:= n-> b(n, n)[1]:
seq(a(n), n=0..60);

Mathematica

b[n_, i_] := b[n, i] = {If[n==i, n, 0], 0} + If[i<1, {0, 0}, b[n, i-1] + If[n<i, {0, 0}, Reverse[b[n-i, i]]]]; a[n_] := b[n, n][[1]]; Table[a[n], {n, 0, 60}] (* Jean-François Alcover, Feb 03 2017, translated from Maple *)
Table[Total[Min/@Select[IntegerPartitions[n], OddQ[Length[#]]&]], {n, 0, 50}] (* Harvey P. Dale, Jul 05 2019 *)

Crossrefs

Cf. A046746, A211373, A222045, A222046, A222047, A222048, A222049.

Sequence in context: A307518 A060773 A330440 * A288937 A327063 A324926

Adjacent sequences: A222041 A222042 A222043 * A222045 A222046 A222047

Keyword

nonn

Author

Alois P. Heinz, Feb 06 2013

Status

approved