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%I #4 Apr 17 2014 14:28:01
%S 0,0,0,0,1,1,3,4,6,10,13,18,24,35,42,61,76,102,127,168,209,271,336,
%T 424,531,661,818,1008,1251,1520,1875,2268,2783,3349,4083,4885,5938,
%U 7078,8539,10154,12203,14456,17281,20427,24312,28670,33968,39951,47176,55363
%N Number of partitions of n such that the number of even parts is a part and the number of odd parts is not a part.
%e a(7) counts these 4 partitions: 4111, 322, 22111, 21111.
%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, A240578, A240579.
%K nonn,easy
%O 0,7
%A _Clark Kimberling_, Apr 10 2014
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