A240202 - OEIS

%I #4 Apr 12 2014 16:22:44

%S 0,0,1,2,3,5,8,12,17,24,34,47,64,87,116,154,202,264,341,443,564,721,

%T 915,1155,1445,1820,2261,2808,3476,4293,5264,6477,7889,9627,11709,

%U 14196,17130,20746,24920,29936,35898,42983,51231,61176,72646,86318,102373,121133

%N Number of partitions p of n such that mean(p) > multiplicity(max(p)).

%F A240200(n) + A116900(n) + a(n) = A000041(n) for n >= 1.

%e a(6) counts these 8 partitions:  6, 51, 42, 411, 33, 321, 3111, 21111.

%t z = 60; f[n_] := f[n] = IntegerPartitions[n];

%t t1 = Table[Count[f[n], p_ /; Mean[p] < Count[p, Max[p]]], {n, 0, z}]  (* A240200 *)

%t t2 = Table[Count[f[n], p_ /; Mean[p] <= Count[p, Max[p]]], {n, 0, z}] (* A240201 *)

%t t3 = Table[Count[f[n], p_ /; Mean[p] == Count[p, Max[p]]], {n, 0, z}] (* A116900 *)

%t t4 = Table[Count[f[n], p_ /; Mean[p] > Count[p, Max[p]]], {n, 0, z}] (* A240202 *)

%t t5 = Table[Count[f[n], p_ /; Mean[p] >= Count[p, Max[p]]], {n, 0, z}] (* A116901 *)

%Y Cf. A240200, A240201, A116900, A116901, A000041.

%K nonn,easy

%O 0,4

%A _Clark Kimberling_, Apr 03 2014