login
Number of partitions of n into distinct parts, where the difference between the number of odd parts and the number of even parts is 10.
2

%I #8 Apr 03 2014 09:34:15

%S 1,0,1,0,2,0,3,0,5,0,7,0,11,0,15,0,22,0,30,0,42,0,55,1,75,2,97,4,128,

%T 7,164,12,212,19,267,30,340,45,423,67,530,97,653,139,807,195,984,271,

%U 1204,370,1456,501,1763,670,2117,889,2543,1167,3032,1522,3618

%N Number of partitions of n into distinct parts, where the difference between the number of odd parts and the number of even parts is 10.

%C With offset 110 number of partitions of n into distinct parts, where the difference between the number of odd parts and the number of even parts is -10.

%H Alois P. Heinz, <a href="/A240146/b240146.txt">Table of n, a(n) for n = 100..1000</a>

%F a(n) = [x^n y^10] Product_{i>=1} 1+x^i*y^(2*(i mod 2)-1).

%e a(104) = 2: [23,17,15,13,11,9,7,5,3,1], [21,19,15,13,11,9,7,5,3,1].

%e a(125) = 2: [23,19,17,15,13,11,9,7,5,3,2,1], [21,19,17,15,13,11,9,7,5,4,3,1].

%p b:= proc(n, i, t) option remember; `if`(n>i*(i+1)/2 or

%p abs(t)>n, 0, `if`(n=0, 1, b(n, i-1, t)+

%p `if`(i>n, 0, b(n-i, i-1, t+(2*irem(i, 2)-1)))))

%p end:

%p a:= n-> b(n$2, -10):

%p seq(a(n), n=100..160);

%Y Column k=10 of A240021.

%K nonn

%O 100,5

%A _Alois P. Heinz_, Apr 02 2014