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%I #4 May 03 2014 11:30:38
%S 0,1,1,2,3,4,6,10,12,18,25,33,45,63,77,107,139,177,231,302,372,486,
%T 612,762,969,1214,1489,1879,2315,2839,3522,4318,5243,6460,7835,9483,
%U 11558,13938,16763,20285,24302,29087,34941,41642,49588,59198,70199,83205,98780
%N Number of partitions p of n such that (number of numbers of the form 3k+1 in p) is a part of p.
%C Each number in p is counted once, regardless of its multiplicity.
%e a(6) counts these 6 partitions: 51, 321, 3111, 2211, 21111, 111111.
%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, A241548.
%K nonn,easy
%O 0,4
%A _Clark Kimberling_, Apr 26 2014
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