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

2,5

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.

Links

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

Example

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].

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 *)

Crossrefs

Column k=2 of A240009.

Sequence in context: A359348 A021993 A324743 * A211228 A338463 A186505

Adjacent sequences: A240008 A240009 A240010 * A240012 A240013 A240014

Keyword

nonn

Author

Alois P. Heinz, Mar 30 2014

Status

approved