A240145 Number of partitions of n into distinct parts, where the difference between the number of odd parts and the number of even parts is 9.

1, 0, 1, 0, 2, 0, 3, 0, 5, 0, 7, 0, 11, 0, 15, 0, 22, 0, 30, 0, 41, 1, 54, 2, 73, 4, 94, 7, 123, 12, 157, 19, 201, 30, 252, 45, 318, 67, 393, 97, 488, 139, 598, 194, 732, 269, 888, 366, 1078, 494, 1296, 658, 1558, 870, 1862, 1137, 2222, 1477, 2639, 1900, 3133

Offset

81,5

Comments

With offset 90 number of partitions of n into distinct parts, where the difference between the number of odd parts and the number of even parts is -9.

Links

Alois P. Heinz, Table of n, a(n) for n = 81..1000

Formula

a(n) = [x^n y^9] Product_{i>=1} 1+x^i*y^(2*(i mod 2)-1).

Example

a(87) = 3: [23,15,13,11,9,7,5,3,1], [21,17,13,11,9,7,5,3,1], [19,17,15,11,9,7,5,3,1].
a(102) = 1: [19,17,15,13,11,9,7,5,3,2,1].

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, -9):
seq(a(n), n=81..145);

Crossrefs

Column k=9 of A240021.

Sequence in context: A240142 A240143 A240144 * A240146 A035363 A241645

Adjacent sequences: A240142 A240143 A240144 * A240146 A240147 A240148

Keyword

nonn

Author

Alois P. Heinz, Apr 02 2014

Status

approved