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 A240492 Number of partitions p of n such that the multiplicity of the median of p is a part of p. 5

%I

%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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Last modified May 28 18:24 EDT 2022. Contains 354122 sequences. (Running on oeis4.)