A240203 - OEIS

%I #4 Apr 12 2014 16:22:52

%S 0,0,1,1,2,3,5,6,9,13,18,25,34,45,62,78,105,140,173,227,298,361,471,

%T 606,725,925,1181,1435,1757,2208,2687,3345,4021,4871,6029,7390,8617,

%U 10558,12924,15535,18112,21987,26372,31838,37245,43875,52729,63184,73092

%N Number of partitions p of n such that mean(p) < multiplicity(min(p)).

%F a(n) + A240205(n) + A240079(n) = A000041(n) for n >= 0.

%e a(6) counts these 5 partitions:  3111, 222, 2211, 21111, 111111.

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

%t t1 = Table[Count[f[n], p_ /; Mean[p] < Count[p, Min[p]]], {n, 0, z}]  (* A240203 *)

%t t2 = Table[Count[f[n], p_ /; Mean[p] <= Count[p, Min[p]]], {n, 0, z}] (* A240204 *)

%t t3 = Table[Count[f[n], p_ /; Mean[p] == Count[p, Min[p]]], {n, 0, z}] (* A240205 *)

%t t4 = Table[Count[f[n], p_ /; Mean[p] > Count[p, Min[p]]], {n, 0, z}] (* A240206 *)

%t t5 = Table[Count[f[n], p_ /; Mean[p] >= Count[p, Min[p]]], {n, 0, z}] (* A240079 *)

%Y Cf. A240204, A240205, A240206, A240079, A000041.

%K nonn,easy

%O 0,5

%A _Clark Kimberling_, Apr 03 2014