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%I #4 Apr 28 2014 17:55:10
%S 1,0,1,1,3,2,4,4,7,7,11,15,21,24,36,45,59,73,99,114,155,183,241,287,
%T 371,433,567,668,842,1003,1270,1483,1856,2205,2707,3210,3940,4627,
%U 5661,6656,8050,9489,11432,13385,16070,18855,22459,26310,31253,36487,43249
%N Number of partitions of n such that the number of parts having multiplicity 1 is not a part and the number of distinct parts is not a part.
%F a(n) + A241446(n) = A000041(n) for n >= 0.
%e a(6) counts these 4 partitions: 6, 51, 33, 222.
%t z = 30; f[n_] := f[n] = IntegerPartitions[n]; u[p_] := Length[DeleteDuplicates[Select[p, Count[p, #] == 1 &]]]; d[p_] := Length[DeleteDuplicates[p]];
%t Table[Count[f[n], p_ /; MemberQ[p, u[p]] && MemberQ[p, d[p]]], {n, 0, z}] (* A241442 *)
%t Table[Count[f[n], p_ /; ! MemberQ[p, u[p]] && MemberQ[p, d[p]] ], {n, 0, z}] (* A241443 *)
%t Table[Count[f[n], p_ /; MemberQ[p, u[p]] && ! MemberQ[p, d[p]] ], {n, 0, z}] (* A241444 *)
%t Table[Count[f[n], p_ /; ! MemberQ[p, u[p]] && ! MemberQ[p, d[p]] ], {n, 0, z}] (* A241445 *)
%t Table[Count[f[n], p_ /; MemberQ[p, u[p]] || MemberQ[p, d[p]] ], {n, 0, z}] (* A241446 *)
%Y Cf. A241442, A241443, A241444, A241446, A000041.
%K nonn,easy
%O 0,5
%A _Clark Kimberling_, Apr 23 2014
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