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A222044 Sum of smallest parts of all partitions of n into an odd number of parts. 8
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified January 22 05:19 EST 2022. Contains 350481 sequences. (Running on oeis4.)