A240019 Number of partitions of n, where the difference between the number of odd parts and the number of even parts is 10.

1, 0, 1, 1, 2, 2, 4, 4, 7, 8, 12, 14, 21, 24, 34, 41, 55, 66, 88, 105, 137, 165, 209, 253, 318, 383, 474, 573, 701, 844, 1027, 1231, 1487, 1780, 2134, 2547, 3041, 3614, 4294, 5092, 6022, 7117, 8389, 9882, 11607, 13638, 15963, 18702, 21834, 25504, 29694, 34600

Offset

10,5

Comments

With offset 20 number of partitions of n, where the difference between the number of odd parts and the number of even parts is -10.

Links

Alois P. Heinz, Table of n, a(n) for n = 10..1000

Example

a(17) = 4: [6,1,1,1,1,1,1,1,1,1,1,1], [5,2,1,1,1,1,1,1,1,1,1,1], [4,3,1,1,1,1,1,1,1,1,1,1], [3,3,2,1,1,1,1,1,1,1,1,1].

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, -10):
seq(a(n), n=10..80);

Crossrefs

Column k=10 of A240009.

Sequence in context: A035979 A240018 A035989 * A036000 A002865 A085811

Adjacent sequences: A240016 A240017 A240018 * A240020 A240021 A240022

Keyword

nonn

Author

Alois P. Heinz, Mar 30 2014

Status

approved