%I #4 Apr 12 2014 16:23:00
%S 0,1,1,1,3,3,6,6,11,14,20,25,38,45,64,85,108,140,190,227,303,387,473,
%T 606,785,926,1183,1496,1816,2208,2778,3345,4170,4990,6031,7424,9097,
%U 10558,12926,15750,18900,21987,26660,31838,38392,44798,52731,63184,75620
%N Number of partitions p of n such that mean(p) <= multiplicity(min(p)).
%F a(n) = A240203(n) + A240205(n) for n >= 0.
%F a(n) + A240206(n) = A000041(n) for n >= 0.
%e a(6) counts these 5 partitions: 411, 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. A240203, A240205, A240206, A240079, A000041.
%K nonn,easy
%O 0,5
%A _Clark Kimberling_, Apr 03 2014