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%I #4 Apr 27 2014 10:23:40
%S 0,0,1,1,2,3,3,5,7,10,14,18,27,32,49,58,80,100,134,167,219,271,351,
%T 433,543,689,848,1051,1298,1609,1945,2413,2930,3566,4321,5266,6302,
%U 7647,9156,11022,13174,15770,18752,22408,26606,31498,37375,44205,52143,61507
%N Number of partitions of n such that the number of parts is not a part and the number of distinct parts is a part.
%F a(n) + A241377(n) + A241379(n) = A241381(n) for n >= 0.
%e a(9) counts these 10 partitions: 522, 3321, 3222, 32211, 321111, 22221, 222111, 221111, 211111, 111111111.
%t z = 30; f[n_] := f[n] = IntegerPartitions[n]; d[p_] := [p] = Length[DeleteDuplicates[p]];
%t Table[Count[f[n], p_ /; MemberQ[p, Length[p]] && MemberQ[p, d[p]]], {n, 0, z}] (* A241377 *)
%t Table[Count[f[n], p_ /; ! MemberQ[p, Length[p]] && MemberQ[p, d[p]]], {n, 0, z}] (* A241378 *)
%t Table[Count[f[n], p_ /; MemberQ[p, Length[p]] && ! MemberQ[p, d[p]]], {n, 0, z}] (* A241379 *)
%t Table[Count[f[n], p_ /; ! MemberQ[p, Length[p]] && ! MemberQ[p, d[p]]], {n, 0, z}] (* A241380 *)
%t Table[Count[f[n], p_ /; MemberQ[p, Length[p]] || MemberQ[p, d[p]]], {n, 0, z}] (* A241381 *)
%Y Cf. A241377, A241379, A241380, A241381.
%K nonn,easy
%O 0,5
%A _Clark Kimberling_, Apr 21 2014
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