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A222045 Sum of smallest parts of all partitions of n into an even number of parts. 8
0, 0, 1, 1, 4, 4, 9, 10, 19, 21, 34, 40, 62, 72, 103, 124, 173, 207, 279, 337, 445, 538, 694, 842, 1077, 1299, 1634, 1977, 2464, 2969, 3669, 4411, 5410, 6488, 7896, 9447, 11442, 13640, 16421, 19536, 23411, 27761, 33124, 39174, 46554, 54915, 65008, 76485, 90258 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

A222044(n) + a(n) = A046746(n).

A222044(n) - a(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) = 9: 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 smallest parts is 1+1+1+3+2+1 = 9.

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)[2]:

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][[2]]; Table[a[n], {n, 0, 60}] (* Jean-Fran├žois Alcover, Feb 03 2017, translated from Maple *)

CROSSREFS

Cf. A046746, A211373, A222044, A222046, A222047, A222048, A222049.

Sequence in context: A192032 A116682 A168157 * A088190 A092322 A341678

Adjacent sequences:  A222042 A222043 A222044 * A222046 A222047 A222048

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Feb 06 2013

STATUS

approved

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Last modified January 22 02:46 EST 2022. Contains 350481 sequences. (Running on oeis4.)