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

0,4

Links

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

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

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 *)

Crossrefs

Cf. A066186, A209423.

Sequence in context: A291724 A340950 A156550 * A007392 A292105 A052401

Adjacent sequences: A208474 A208475 A208476 * A208478 A208479 A208480

Keyword

nonn

Author

Omar E. Pol, Mar 10 2012

Extensions

More terms from Alois P. Heinz, Mar 10 2012

Status

approved