A240146 Number of partitions of n into distinct parts, where the difference between the number of odd parts and the number of even parts is 10.

1, 0, 1, 0, 2, 0, 3, 0, 5, 0, 7, 0, 11, 0, 15, 0, 22, 0, 30, 0, 42, 0, 55, 1, 75, 2, 97, 4, 128, 7, 164, 12, 212, 19, 267, 30, 340, 45, 423, 67, 530, 97, 653, 139, 807, 195, 984, 271, 1204, 370, 1456, 501, 1763, 670, 2117, 889, 2543, 1167, 3032, 1522, 3618

Offset

100,5

Comments

With offset 110 number of partitions of n into distinct parts, 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 = 100..1000

Formula

a(n) = [x^n y^10] Product_{i>=1} 1+x^i*y^(2*(i mod 2)-1).

Example

a(104) = 2: [23,17,15,13,11,9,7,5,3,1], [21,19,15,13,11,9,7,5,3,1].
a(125) = 2: [23,19,17,15,13,11,9,7,5,3,2,1], [21,19,17,15,13,11,9,7,5,4,3,1].

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, -10):
seq(a(n), n=100..160);

Crossrefs

Column k=10 of A240021.

Sequence in context: A240143 A240144 A240145 * A035363 A241645 A266774

Adjacent sequences: A240143 A240144 A240145 * A240147 A240148 A240149

Keyword

nonn

Author

Alois P. Heinz, Apr 02 2014

Status

approved