%I #4 Apr 17 2014 14:29:53
%S 0,0,0,1,1,2,2,3,4,5,8,10,14,16,25,28,40,47,65,77,101,122,158,193,239,
%T 295,363,449,539,670,800,989,1169,1439,1701,2083,2442,2975,3493,4224,
%U 4941,5944,6955,8313,9706,11538,13475,15936,18568,21859,25466,29847
%N Number of partitions of n such that the number of even parts is a part and the number of odd parts is a part.
%e a(10) counts these 8 partitions: 721, 6211, 5221, 4321, 43111, 421111, 3322, 32221.
%t z = 62; f[n_] := f[n] = IntegerPartitions[n];
%t Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 0]]], {n, 0, z}] (* A240573 *)
%t Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240574 *)
%t Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 0]] && MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240575 *)
%t Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 0]]  MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240576 *)
%t Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 0]] && ! MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240577 *)
%t Table[Count[f[n], p_ /; ! MemberQ[p, Count[Mod[p, 2], 0]] && MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240578 *)
%t Table[Count[f[n], p_ /; ! MemberQ[p, Count[Mod[p, 2], 0]] && ! MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240579 *)
%Y Cf. A240573, A240574, A240576, A240577, A240578, A240579.
%K nonn,easy
%O 0,6
%A _Clark Kimberling_, Apr 10 2014
