A240011 Number of partitions of n, where the difference between the number of odd parts and the number of even parts is 2.

1, 0, 1, 1, 2, 2, 3, 4, 5, 8, 8, 13, 14, 21, 23, 34, 37, 52, 60, 79, 93, 120, 143, 178, 216, 263, 321, 386, 470, 560, 684, 806, 980, 1154, 1395, 1636, 1969, 2304, 2758, 3225, 3835, 4480, 5305, 6186, 7288, 8495, 9961, 11594, 13545, 15742, 18325, 21269, 24675

Offset: 2

Author

Alois P. Heinz, Mar 30 2014

Keywords

• nonn

Comments

With offset 4 number of partitions of n, where the difference between the number of odd parts and the number of even parts is -2.

Examples

			a(10) = 5: [9,1], [7,3], [5,5], [4,2,1,1,1,1], [3,2,2,1,1,1].
a(11) = 8: [8,1,1,1], [7,2,1,1], [6,3,1,1], [5,4,1,1], [5,3,2,1], [4,3,3,1], [3,3,3,2], [2,2,2,1,1,1,1,1].
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 2..1000

Crossrefs

Column k=2 of A240009.

Programs

Maple

b:= proc(n, i, t) option remember; `if`(abs(t)>n, 0,
      `if`(n=0, 1, `if`(i<1, 0, b(n, i-1, t)+
      `if`(i>n, 0, b(n-i, i, t+(2*irem(i, 2)-1))))))
    end:
a:= n-> b(n$2, -2):
seq(a(n), n=2..80);

Mathematica

b[n_, i_, t_] := b[n, i, t] = If[Abs[t] > n, 0, If[n == 0, 1, If[i < 1, 0, b[n, i - 1, t] + If[i > n, 0, b[n - i, i, t + 2 Mod[i, 2] - 1]]]]];
a[n_] := b[n, n, -2];
a /@ Range[2, 80] (* Jean-François Alcover, Dec 10 2020, after Alois P. Heinz *)