A240493 - OEIS

%I #6 Aug 01 2014 13:41:34

%S 0,1,0,1,3,2,4,6,9,13,18,21,34,42,58,74,104,124,171,210,278,346,448,

%T 546,711,866,1094,1338,1684,2036,2546,3074,3798,4583,5618,6741,8237,

%U 9848,11927,14246,17177,20418,24516,29067,34719,41078,48856,57605,68310

%N Number of partitions of n such that the multiplicity of the least part is a part.

%e a(6) counts these 4 partitions:  51, 321, 3111, 2211.

%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