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A240014 Number of partitions of n, where the difference between the number of odd parts and the number of even parts is 5.

%I A240014 #11 Dec 10 2020 17:35:11
%S A240014 1,0,1,1,2,2,4,4,7,8,12,14,20,24,32,41,51,65,81,102,125,158,190,239,
%T A240014 287,357,426,528,626,769,913,1110,1314,1590,1877,2255,2660,3174,3738,
%U A240014 4439,5215,6162,7230,8502,9954,11666,13626,15911,18551,21590,25118,29154
%N A240014 Number of partitions of n, where the difference between the number of odd parts and the number of even parts is 5.
%C A240014 With offset 10 number of partitions of n, where the difference between the number of odd parts and the number of even parts is -5.
%H A240014 Alois P. Heinz, <a href="/A240014/b240014.txt">Table of n, a(n) for n = 5..1000</a>
%p A240014 b:= proc(n, i, t) option remember; `if`(abs(t)>n, 0,
%p A240014       `if`(n=0, 1, `if`(i<1, 0, b(n, i-1, t)+
%p A240014       `if`(i>n, 0, b(n-i, i, t+(2*irem(i, 2)-1))))))
%p A240014     end:
%p A240014 a:= n-> b(n$2, -5):
%p A240014 seq(a(n), n=5..80);
%t A240014 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 A240014 a[n_] := b[n, n, -5];
%t A240014 a /@ Range[5, 80] (* _Jean-François Alcover_, Dec 10 2020, after _Alois P. Heinz_ *)
%Y A240014 Column k=5 of A240009.
%K A240014 nonn
%O A240014 5,5
%A A240014 _Alois P. Heinz_, Mar 30 2014