A240010 Number of partitions of n, where the difference between the number of odd parts and the number of even parts is 1.

1, 0, 1, 1, 1, 2, 2, 4, 3, 7, 6, 11, 11, 17, 19, 27, 31, 41, 51, 62, 79, 95, 121, 142, 182, 212, 269, 314, 393, 459, 570, 665, 816, 958, 1160, 1364, 1639, 1928, 2297, 2706, 3200, 3768, 4434, 5212, 6105, 7170, 8361, 9799, 11396, 13322, 15450, 18022, 20850

Offset

1,6

Comments

With offset 2 number of partitions of n, where the difference between the number of odd parts and the number of even parts is -1.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Example

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

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, -1):
seq(a(n), n=1..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, -1];
Array[a, 80] (* Jean-François Alcover, Dec 10 2020, after Alois P. Heinz *)

Crossrefs

Column k=1 of A240009.

Sequence in context: A325690 A238779 A239832 * A283502 A324756 A324754

Adjacent sequences: A240007 A240008 A240009 * A240011 A240012 A240013

Keyword

nonn

Author

Alois P. Heinz, Mar 30 2014

Status

approved