A240142 Number of partitions of n into distinct parts, where the difference between the number of odd parts and the number of even parts is 6.

1, 0, 1, 0, 2, 0, 3, 0, 5, 0, 7, 0, 11, 0, 14, 1, 20, 2, 26, 4, 35, 7, 44, 12, 58, 19, 71, 30, 90, 45, 110, 66, 136, 94, 164, 132, 201, 181, 240, 246, 291, 328, 348, 433, 419, 564, 501, 728, 605, 929, 726, 1177, 878, 1477, 1061, 1841, 1288, 2278, 1565, 2801

Offset

36,5

Comments

With offset 42 number of partitions of n into distinct parts, where the difference between the number of odd parts and the number of even parts is -6.

Links

Alois P. Heinz, Table of n, a(n) for n = 36..1000

Formula

a(n) = [x^n y^6] Product_{i>=1} 1+x^i*y^(2*(i mod 2)-1).

Example

a(50) = 14: [25,9,7,5,3,1], [23,11,7,5,3,1], [21,13,7,5,3,1], [21,11,9,5,3,1], [19,15,7,5,3,1], [19,13,9,5,3,1], [19,11,9,7,3,1], [17,15,9,5,3,1], [17,13,11,5,3,1], [17,13,9,7,3,1], [17,11,9,7,5,1], [15,13,11,7,3,1], [15,13,9,7,5,1], [15,11,9,7,5,3].
a(51) = 1: [13,11,9,7,5,3,2,1].

Maple

b:= proc(n, i, t) option remember; `if`(n>i*(i+1)/2 or
      abs(t)>n, 0, `if`(n=0, 1, b(n, i-1, t)+
      `if`(i>n, 0, b(n-i, i-1, t+(2*irem(i, 2)-1)))))
    end:
a:= n-> b(n$2, -6):
seq(a(n), n=36..120);

Crossrefs

Column k=6 of A240021.

Sequence in context: A240140 A240141 A049641 * A240143 A240144 A240145

Adjacent sequences: A240139 A240140 A240141 * A240143 A240144 A240145

Keyword

nonn

Author

Alois P. Heinz, Apr 02 2014

Status

approved