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%I #4 May 03 2014 11:30:47
%S 0,0,0,1,1,2,4,7,8,15,21,29,42,60,76,107,144,186,246,326,409,532,683,
%T 856,1083,1374,1698,2121,2644,3244,3998,4930,5995,7316,8927,10782,
%U 13043,15778,18932,22729,27289,32549,38833,46316,54951,65172,77290,91239
%N Number of partitions p of n such that (number of numbers of the form 3k+2 in p) is a part of p.
%C Each number in p is counted once, regardless of its multiplicity.
%e a(6) counts these 4 partitions: 51, 321, 2211, 21111.
%t z = 30; f[n_] := f[n] = IntegerPartitions[n]; s[k_, p_] := Count[Mod[DeleteDuplicates[p], 3], k]
%t Table[Count[f[n], p_ /; MemberQ[p, s[0, p]]], {n, 0, z}] (* A241546 *)
%t Table[Count[f[n], p_ /; MemberQ[p, s[1, p]]], {n, 0, z}] (* A241547 *)
%t Table[Count[f[n], p_ /; MemberQ[p, s[2, p]]], {n, 0, z}] (* A241548 *)
%Y Cf. A241546, A241547.
%K nonn,easy
%O 0,6
%A _Clark Kimberling_, Apr 26 2014
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