A240495 - OEIS

%I #6 Aug 01 2014 13:42:29

%S 0,0,0,1,1,1,2,2,5,5,8,10,16,19,25,33,46,53,72,89,114,141,183,217,278,

%T 339,421,510,632,759,931,1124,1361,1636,1977,2354,2830,3378,4034,4781,

%U 5695,6732,7975,9420,11098,13063,15376,18014,21124,24716,28883,33697

%N Number of partitions p of n such that the multiplicity of (max(p) - min(p)) is a part.

%e a(8) counts these 5 partitions:  431, 422, 3221, 32111, 22211.

%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 - A240494.

%K nonn,easy

%O 0,7

%A _Clark Kimberling_, Apr 06 2014