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%I #6 Aug 01 2014 13:41:06
%S 0,1,0,0,2,1,2,2,7,8,13,13,22,25,37,46,69,80,116,138,187,226,301,363,
%T 481,585,750,912,1163,1404,1768,2132,2654,3199,3948,4743,5823,6976,
%U 8496,10158,12306,14656,17661,20986,25154,29814,35578,42042,49996,58930
%N Number of partitions p of n such that the multiplicity of the median of p is a part of p.
%e a(8) counts these 7 partitions: 521, 431, 422, 41111, 332, 3221, 32111.
%t z = 60; f[n_] := f[n] = IntegerPartitions[n];
%t Table[Count[f[n], p_ /; MemberQ[p, Count[p, Mean[p]]]], {n, 0, z}] (* A240491 *)
%t Table[Count[f[n], p_ /; MemberQ[p, Count[p, Median[p]]]], {n, 0, z}] (* A240492 *)
%t Table[Count[f[n], p_ /; MemberQ[p, Count[p, Min[p]]]], {n, 0, z}] (* A240493 *)
%t Table[Count[f[n], p_ /; MemberQ[p, Count[p, Max[p]]]], {n, 0, z}] (* A240494 *)
%t Table[Count[f[n], p_ /; MemberQ[p, Count[p, Max[p] - Min[p]]]], {n, 0, z}] (* A240495 *)
%Y Cf. A240491 - A240495.
%K nonn,easy
%O 0,5
%A _Clark Kimberling_, Apr 06 2014
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