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%I #5 May 03 2014 11:30:26
%S 0,0,0,0,1,1,2,4,6,9,13,20,28,39,55,75,99,136,179,237,308,403,515,666,
%T 847,1079,1357,1717,2143,2680,3325,4128,5084,6270,7678,9402,11452,
%U 13949,16895,20467,24682,29746,35709,42848,51227,61200,72896,86738,102926
%N Number of partitions p of n such that (number of numbers of the form 3k in p) is a part of p.
%C Each number in p is counted once, regardless of its multiplicity.
%e a(6) counts these 2 partitions: 321, 3111.
%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. A241547, A241548.
%K nonn,easy
%O 0,7
%A _Clark Kimberling_, Apr 26 2014
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