A240184 - OEIS

%I #8 Apr 12 2014 16:22:11

%S 0,0,1,2,2,5,6,11,14,20,29,41,52,76,98,130,170,227,288,378,477,615,

%T 778,985,1228,1551,1928,2399,2964,3670,4498,5538,6755,8251,10027,

%U 12175,14715,17802,21420,25764,30886,37009,44181,52731,62730,74570,88435,104762

%N Number of partitions of n such that (greatest part) > (multiplicity of least part).

%F A240178(n) + A240183(n) + a(n ) = A000041(n) for n >= 1.

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

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

%t t1 = Table[Count[f[n], p_ /; Max[p] < Count[p, Min[p]]], {n, 0, z}]  (* A240178 *)

%t t2 = Table[Count[f[n], p_ /; Max[p] <= Count[p, Min[p]]], {n, 0, z}] (* A240182 *)

%t t3 = Table[Count[f[n], p_ /; Max[p] == Count[p, Min[p]]], {n, 0, z}] (* A240183 *)

%t t4 = Table[Count[f[n], p_ /; Max[p] > Count[p, Min[p]]], {n, 0, z}] (* A240184 *)

%t t5 = Table[Count[f[n], p_ /; Max[p] >= Count[p, Min[p]]], {n, 0, z}] (* A240179 *)

%Y Cf. A240178, A240182, A240183, A240179, A000041.

%K nonn,easy

%O 0,4

%A _Clark Kimberling_, Apr 02 2014