cp's OEIS Frontend

A171967 Number of partitions of n with distinct numbers of odd and even parts.

%I A171967 #12 Oct 27 2018 19:42:04
%S A171967 0,1,2,2,5,5,10,12,20,25,37,49,68,90,119,158,206,269,344,446,565,722,
%T A171967 908,1148,1435,1795,2229,2765,3416,4204,5164,6315,7717,9380,11406,
%U A171967 13793,16692,20093,24203,29012,34799,41552,49636,59059,70279,83341,98822
%N A171967 Number of partitions of n with distinct numbers of odd and even parts.
%C A171967 a(n) = A000041(n) - A045931(n) = A108949(n) + A108950(n).
%C A171967 a(n) = Sum_{k<>0} A240009(n,k). - _Alois P. Heinz_, Mar 30 2014
%H A171967 Alois P. Heinz, <a href="/A171967/b171967.txt">Table of n, a(n) for n = 0..3500</a>
%p A171967 b:= proc(n, i, t) option remember; `if`(n=0,
%p A171967       `if`(t<>0, 1, 0), `if`(i<1, 0, b(n, i-1, t)+
%p A171967       `if`(i>n, 0, b(n-i, i, t+(2*irem(i, 2)-1)))))
%p A171967     end:
%p A171967 a:= n-> b(n$2, 0):
%p A171967 seq(a(n), n=0..80);  # _Alois P. Heinz_, Mar 30 2014
%t A171967 $RecursionLimit = 1000; b[n_, i_, t_] := b[n, i, t] = If[n==0, If[t != 0, 1, 0], If[i < 1, 0, b[n, i-1, t] + If[i>n, 0, b[n-i, i, t+(2*Mod[i, 2]-1)]]]]; a[n_] := b[n, n, 0]; Table[a[n], {n, 0, 80}] (* _Jean-François Alcover_, Jun 30 2015, after _Alois P. Heinz_ *)
%Y A171967 Cf. A130780, A171966.
%K A171967 nonn
%O A171967 0,3
%A A171967 _Reinhard Zumkeller_, Jan 21 2010