This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A241412 #5 Apr 28 2014 18:38:17
%S A241412 1,0,1,1,3,2,4,4,7,7,11,14,19,21,30,38,51,59,81,98,124,156,199,239,
%T A241412 311,365,468,572,711,844,1070,1271,1572,1884,2318,2749,3387,4000,4879,
%U A241412 5796,6977,8266,9986,11769,14071,16632,19800,23300,27700,32471,38447
%N A241412 Number of partitions of n such that neither the number of parts having multiplicity >1 nor the number of distinct parts is a part.
%C A241412 As used here, the term "distinct parts" includes each number, once, that occurs more than once; e.g., the distinct parts of the partition {4,3,3,1,1,1} are 4, 3, 1.
%e A241412 a(6) counts these 4 partitions: 6, 51, 33, 222.
%t A241412 z = 30; f[n_] := f[n] = IntegerPartitions[n]; e[p_] := Length[DeleteDuplicates[Select[p, Count[p, #] > 1 &]]]; d[p_] := Length[DeleteDuplicates[p]];
%t A241412 Table[Count[f[n], p_ /; MemberQ[p, e[p]]], {n, 0, z}] (* A241408 *)
%t A241412 Table[Count[f[n], p_ /; MemberQ[p, e[p]] && MemberQ[p, d[p]]], {n, 0, z}] (* A241409 *)
%t A241412 Table[Count[f[n], p_ /; ! MemberQ[p, e[p]] && MemberQ[p, d[p]] ], {n, 0, z}] (* A241410 *)
%t A241412 Table[Count[f[n], p_ /; MemberQ[p, e[p]] && ! MemberQ[p, d[p]] ], {n, 0, z}] (* A241411 *)
%t A241412 Table[Count[f[n], p_ /; ! MemberQ[p, e[p]] && ! MemberQ[p, d[p]] ], {n, 0, z}] (* A241412 *)
%Y A241412 Cf. A241408, A241409, A241410, A241411.
%K A241412 nonn,easy
%O A241412 0,5
%A A241412 _Clark Kimberling_, Apr 22 2014