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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Apr 02 2014
STATUS
approved