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%I #4 Apr 14 2014 11:14:15
%S 0,0,0,0,0,1,0,0,1,1,1,2,2,2,5,5,6,9,9,13,17,21,25,32,39,48,59,73,87,
%T 109,129,156,190,226,271,328,388,463,552,654,772,919,1078,1271,1500,
%U 1760,2059,2418,2820,3296,3844,4475,5198,6048,7006,8121,9400,10866
%N Number of partitions of n such that the multiplicity of 2*(number of parts) is a part.
%e a(14) counts these 5 partitions: [10,1111, [8,4,1,1], [8,3,2,1], [7,6,1], [6,6,2].
%t z = 60; f[n_] := f[n] = IntegerPartitions[n];
%t Table[Count[f[n], p_ /; MemberQ[p, Count[p, 2*Min[p]]]], {n, 0, z}] (* A240496 *)
%t Table[Count[f[n], p_ /; MemberQ[p, Count[p, (Min[p] + Max[p])/2]]], {n, 1, z}] (* A240497 *)
%t Table[Count[f[n], p_ /; MemberQ[p, Count[p, Min[p]*Max[p]]]], {n, 0, z}] (* A240498 *)
%t Table[Count[f[n], p_ /; MemberQ[p, Count[p, Length[p]]]], {n, 0, z}] (* A240499 *)
%t Table[Count[f[n], p_ /; MemberQ[p, Count[p, 2*Length[p]]]], {n, 0, z}] (* A240500 *)
%Y Cf. A240496, A240497, A240498, A240499.
%K nonn,easy
%O 0,12
%A _Clark Kimberling_, Apr 06 2014
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