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A208477 Difference between the sum of odd parts and the sum of even parts in all the partitions of n. 1
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Aug 29 2016, after Alois P. Heinz *)

CROSSREFS

Cf. A066186, A209423.

Sequence in context: A291724 A156550 A088307 * 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

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Last modified September 16 08:36 EDT 2019. Contains 327091 sequences. (Running on oeis4.)