A171967 - OEIS

%I #12 Oct 27 2018 19:42:04

%S 0,1,2,2,5,5,10,12,20,25,37,49,68,90,119,158,206,269,344,446,565,722,

%T 908,1148,1435,1795,2229,2765,3416,4204,5164,6315,7717,9380,11406,

%U 13793,16692,20093,24203,29012,34799,41552,49636,59059,70279,83341,98822

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

%C a(n) = A000041(n) - A045931(n) = A108949(n) + A108950(n).

%C a(n) = Sum_{k<>0} A240009(n,k). - _Alois P. Heinz_, Mar 30 2014

%H Alois P. Heinz, <a href="/A171967/b171967.txt">Table of n, a(n) for n = 0..3500</a>

%p b:= proc(n, i, t) option remember; `if`(n=0,

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

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

%p     end:

%p a:= n-> b(n$2, 0):

%p seq(a(n), n=0..80);  # _Alois P. Heinz_, Mar 30 2014

%t $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 Cf. A130780, A171966.

%K nonn

%O 0,3

%A _Reinhard Zumkeller_, Jan 21 2010