Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #4 Apr 29 2014 22:46:36
%S 1,0,0,1,2,3,3,4,5,6,8,12,16,23,27,41,46,63,71,96,109,148,161,219,256,
%T 332,379,500,580,738,859,1079,1250,1560,1791,2220,2563,3116,3595,4369,
%U 5054,6080,7020,8418,9729,11617,13409,15911,18417,21713,25078,29467
%N Number of partitions p of n such that #m(1) = #m(2), where #m(i) = number of numbers in p that have multiplicity i.
%e a(6) counts these 3 partitions: 411, 222, 111111.
%t z = 30; u[p_] := Length[DeleteDuplicates[Select[p, Count[p, #] == 1 &]]]; v[p_] := Length[DeleteDuplicates[Select[p, Count[p, #] == 2 &]]]; Table[Count[IntegerPartitions[n], p_ /; u[p] == v[p]], {n, 0, z}]
%Y Cf. A241274.
%K nonn,easy
%O 0,5
%A _Clark Kimberling_, Apr 24 2014