A240144 Number of partitions of n into distinct parts, where the difference between the number of odd parts and the number of even parts is 8.

1, 0, 1, 0, 2, 0, 3, 0, 5, 0, 7, 0, 11, 0, 15, 0, 22, 0, 29, 1, 40, 2, 52, 4, 70, 7, 89, 12, 116, 19, 146, 30, 186, 45, 230, 67, 288, 97, 352, 138, 434, 192, 526, 265, 640, 359, 769, 482, 928, 639, 1107, 840, 1325, 1092, 1574, 1410, 1874, 1803, 2218, 2291

Offset

64,5

Comments

With offset 72 number of partitions of n into distinct parts, where the difference between the number of odd parts and the number of even parts is -8.

Links

Alois P. Heinz, Table of n, a(n) for n = 64..1000

Formula

a(n) = [x^n y^8] Product_{i>=1} 1+x^i*y^(2*(i mod 2)-1).

Example

a(70) = 3: [21,13,11,9,7,5,3,1], [19,15,11,9,7,5,3,1], [17,15,13,9,7,5,3,1].
a(85) = 2: [19,15,13,11,9,7,5,3,2,1], [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, -8):
seq(a(n), n=64..130);

Crossrefs

Column k=8 of A240021.

Sequence in context: A049641 A240142 A240143 * A240145 A240146 A035363

Adjacent sequences: A240141 A240142 A240143 * A240145 A240146 A240147

Keyword

nonn

Author

Alois P. Heinz, Apr 02 2014

Status

approved