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%I #7 Apr 17 2014 14:30:09
%S 1,0,2,2,3,3,6,6,10,9,18,20,30,32,53,60,82,100,138,172,216,277,346,
%T 455,533,709,834,1117,1262,1705,1927,2596,2875,3872,4289,5763,6294,
%U 8429,9221,12286,13320,17685,19184,25333,27332,35931,38770,50728,54516,710069
%N Number of partitions of n such that the number of odd parts is not a part and the number of even parts is not a part.
%e a(7) counts these 6 partitions: 7, 52, 511, 43, 31111, 1111111.
%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, A240575, A240576, A240577, A240578.
%K nonn,easy
%O 0,3
%A _Clark Kimberling_, Apr 10 2014
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