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A240013 Number of partitions of n, where the difference between the number of odd parts and the number of even parts is 4.

%I A240013 #12 Dec 10 2020 17:35:31
%S A240013 1,0,1,1,2,2,4,4,7,8,11,14,19,24,30,40,48,63,76,98,117,151,178,227,
%T A240013 269,337,399,496,586,720,854,1036,1228,1481,1752,2096,2480,2946,3481,
%U A240013 4115,4850,5707,6717,7868,9237,10789,12632,14707,17181,19947,23243,26925
%N A240013 Number of partitions of n, where the difference between the number of odd parts and the number of even parts is 4.
%C A240013 With offset 8 number of partitions of n, where the difference between the number of odd parts and the number of even parts is -4.
%H A240013 Alois P. Heinz, <a href="/A240013/b240013.txt">Table of n, a(n) for n = 4..1000</a>
%p A240013 b:= proc(n, i, t) option remember; `if`(abs(t)>n, 0,
%p A240013       `if`(n=0, 1, `if`(i<1, 0, b(n, i-1, t)+
%p A240013       `if`(i>n, 0, b(n-i, i, t+(2*irem(i, 2)-1))))))
%p A240013     end:
%p A240013 a:= n-> b(n$2, -4):
%p A240013 seq(a(n), n=4..80);
%t A240013 b[n_, i_, t_] := b[n, i, t] = If[Abs[t] > n, 0, If[n == 0, 1, If[i < 1, 0, b[n, i - 1, t] + If[i > n, 0, b[n - i, i, t + 2 Mod[i, 2] - 1]]]]];
%t A240013 a[n_] := b[n, n, -4];
%t A240013 a /@ Range[4, 80] (* _Jean-François Alcover_, Dec 10 2020, after _Alois P. Heinz_ *)
%Y A240013 Column k=4 of A240009.
%K A240013 nonn
%O A240013 4,5
%A A240013 _Alois P. Heinz_, Mar 30 2014