A240143 Number of partitions of n into distinct parts, where the difference between the number of odd parts and the number of even parts is 7.

1, 0, 1, 0, 2, 0, 3, 0, 5, 0, 7, 0, 11, 0, 15, 0, 21, 1, 28, 2, 38, 4, 49, 7, 65, 12, 82, 19, 105, 30, 131, 45, 164, 67, 201, 96, 248, 136, 301, 188, 366, 258, 441, 347, 531, 463, 635, 609, 761, 795, 907, 1025, 1082, 1313, 1289, 1665, 1537, 2099, 1831, 2624

Offset

49,5

Comments

With offset 56 number of partitions of n into distinct parts, where the difference between the number of odd parts and the number of even parts is -7.

Links

Alois P. Heinz, Table of n, a(n) for n = 49..1000

Formula

a(n) = [x^n y^7] Product_{i>=1} 1+x^i*y^(2*(i mod 2)-1).

Example

a(59) = 7: [23,11,9,7,5,3,1], [21,13,9,7,5,3,1], [19,15,9,7,5,3,1], [19,13,11,7,5,3,1], [17,15,11,7,5,3,1], [17,13,11,9,5,3,1], [15,13,11,9,7,3,1].
a(70) = 4: [19,13,11,9,7,5,3,2,1], [17,15,11,9,7,5,3,2,1], [17,13,11,9,7,5,4,3,1], [15,13,11,9,7,6,5,3,1].

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, -7):
seq(a(n), n=49..120);

Crossrefs

Column k=7 of A240021.

Sequence in context: A240141 A049641 A240142 * A240144 A240145 A240146

Adjacent sequences: A240140 A240141 A240142 * A240144 A240145 A240146

Keyword

nonn

Author

Alois P. Heinz, Apr 02 2014

Status

approved