cp's OEIS Frontend

A222047 Sum of largest parts of all partitions of n into an odd number of parts.

%I A222047 #15 Aug 30 2016 03:51:55
%S A222047 0,1,2,4,6,11,17,28,41,66,93,140,195,282,384,541,722,992,1311,1762,
%T A222047 2299,3045,3929,5127,6559,8458,10726,13689,17225,21780,27224,34134,
%U A222047 42387,52769,65138,80544,98887,121538,148456,181456,220590,268252,324677,392961
%N A222047 Sum of largest parts of all partitions of n into an odd number of parts.
%C A222047 a(n) + A222048(n) = A006128(n).
%C A222047 a(n) - A222048(n) = A222049(n).
%H A222047 Alois P. Heinz, <a href="/A222047/b222047.txt">Table of n, a(n) for n = 0..1000</a>
%e A222047 a(6) = 17: 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 largest parts is 2+2+3+4+6 = 17.
%p A222047 b:= proc(n, i) option remember; [`if`(n=i, n, 0), 0]+
%p A222047       `if`(i>n, [0, 0], b(n, i+1)+(l-> [l[2], l[1]])(b(n-i, i)))
%p A222047     end:
%p A222047 a:= n-> b(n,1)[1]:
%p A222047 seq(a(n), n=0..50);
%t A222047 Table[Total[Max[#]&/@Select[IntegerPartitions[n],OddQ[Length[#]]&]],{n,0,50}] (* _Harvey P. Dale_, Apr 19 2014 *)
%t A222047 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][[1]]; Table[a[n], {n, 0, 50}] (* _Jean-François Alcover_, Aug 30 2016, after _Alois P. Heinz_ *)
%Y A222047 Cf. A006128, A211373, A222044, A222045, A222046, A222048, A222049.
%K A222047 nonn
%O A222047 0,3
%A A222047 _Alois P. Heinz_, Feb 06 2013