|
%I #8 Apr 03 2014 09:33:22
%S 1,0,1,0,2,0,3,0,5,0,7,0,11,0,14,1,20,2,26,4,35,7,44,12,58,19,71,30,
%T 90,45,110,66,136,94,164,132,201,181,240,246,291,328,348,433,419,564,
%U 501,728,605,929,726,1177,878,1477,1061,1841,1288,2278,1565,2801
%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 6.
%C With offset 42 number of partitions of n into distinct parts, where the difference between the number of odd parts and the number of even parts is -6.
%H Alois P. Heinz, <a href="/A240142/b240142.txt">Table of n, a(n) for n = 36..1000</a>
%F a(n) = [x^n y^6] Product_{i>=1} 1+x^i*y^(2*(i mod 2)-1).
%e a(50) = 14: [25,9,7,5,3,1], [23,11,7,5,3,1], [21,13,7,5,3,1], [21,11,9,5,3,1], [19,15,7,5,3,1], [19,13,9,5,3,1], [19,11,9,7,3,1], [17,15,9,5,3,1], [17,13,11,5,3,1], [17,13,9,7,3,1], [17,11,9,7,5,1], [15,13,11,7,3,1], [15,13,9,7,5,1], [15,11,9,7,5,3].
%e a(51) = 1: [13,11,9,7,5,3,2,1].
%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, -6):
%p seq(a(n), n=36..120);
%Y Column k=6 of A240021.
%K nonn
%O 36,5
%A _Alois P. Heinz_, Apr 02 2014
|
