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

Author

Alois P. Heinz, Apr 02 2014

Keywords

• nonn

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.

Examples

			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].
		

Links

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

Crossrefs

Column k=7 of A240021.

Programs

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);

Formula

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