A208477 Difference between the sum of odd parts and the sum of even parts in all the partitions of n.

0, 1, 0, 5, 0, 11, 6, 25, 12, 50, 40, 96, 80, 173, 170, 320, 316, 545, 590, 930, 1020, 1552, 1760, 2537, 2900, 4066, 4736, 6450, 7540, 10045, 11856, 15482, 18280, 23555, 27920, 35461, 42032, 52805, 62662, 77955, 92380, 113963, 135040, 165295, 195540, 237866

Offset: 0

Author

Omar E. Pol, Mar 10 2012

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A066186, A209423.

Programs

Maple

b:= proc(n,i) option remember; local g, h;
      if n=0 then [1, 0]
    elif i<1 then [0, 0]
    else g:= b(n, i-1);
         h:= `if`(i>n, [0, 0], b(n-i, i));
         [g[1]+h[1], g[2]+h[2] +h[1]*i*(2*(i mod 2)-1)]
      fi
    end:
a:= n-> b(n, n)[2]:
seq(a(n), n=0..60); # Alois P. Heinz, Mar 10 2012

Mathematica

Map[Total[Select[#, OddQ]] - Total[Select[#, EvenQ]] &[Flatten[IntegerPartitions[#]]] &, -1 + Range[30]] (* Peter J. C. Moses, Mar 14 2014 *)
max = 60; s = Sum[x^(2i) (x^(2i) - 2i (x-1) - 1)/(x + x^(4i) - (x+1) x^(2i) ), {i, 1, Floor[max/2]}]/QPochhammer[x] + O[x]^max; CoefficientList[s, x] (* Jean-François Alcover, Aug 29 2016, after Alois P. Heinz *)

Formula

a(n) = A066967(n) - A066966(n).

G.f.: (Sum_{i>0} (2*i-1)*x^(2*i-1)/(1-x^(2*i-1))-2*i*x^(2*i)/(1-x^(2*i))) / Product_{j>0} (1-x^j). - Alois P. Heinz, Mar 10 2012

Extensions

More terms from Alois P. Heinz, Mar 10 2012