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

%I A222048 #10 Feb 02 2017 04:18:35
%S A222048 0,0,1,2,6,9,18,26,45,62,99,135,204,274,396,527,741,973,1333,1736,
%T A222048 2331,3007,3970,5079,6615,8393,10796,13605,17320,21673,27339,34001,
%U A222048 42540,52597,65324,80332,99127,121274,148745,181131,220956,267852,325114,392476,474178
%N A222048 Sum of largest parts of all partitions of n into an even number of parts.
%C A222048 A222047(n) + a(n) = A006128(n).
%C A222048 A222047(n) - a(n) = A222049(n).
%H A222048 Alois P. Heinz, <a href="/A222048/b222048.txt">Table of n, a(n) for n = 0..1000</a>
%e A222048 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.
%p A222048 b:= proc(n, i) option remember; [`if`(n=i, n, 0), 0]+
%p A222048       `if`(i>n, [0, 0], b(n, i+1)+(l-> [l[2], l[1]])(b(n-i, i)))
%p A222048     end:
%p A222048 a:= n-> b(n,1)[2]:
%p A222048 seq(a(n), n=0..50);
%t A222048 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 *)
%Y A222048 Cf. A006128, A211373, A222044, A222045, A222046, A222047, A222049.
%K A222048 nonn
%O A222048 0,4
%A A222048 _Alois P. Heinz_, Feb 06 2013