A240304 - OEIS

%I #6 Apr 12 2014 16:25:35

%S 0,0,0,0,0,1,0,2,3,4,5,12,11,21,27,37,49,71,87,124,153,204,260,344,

%T 421,550,685,867,1076,1360,1660,2081,2544,3145,3831,4706,5692,6958,

%U 8395,10171,12224,14761,17645,21204,25281,30207,35914,42760,50618,60057,70914

%N Number of partitions of n such that (maximal multiplicity of parts) > (multiplicity of the least part).

%F a(n) + A240303(n) = A000041(n) for n >= 1.

%e a(7) counts these 2 partitions of 7: 331, 2221.

%t z = 60; f[n_] := f[n] = IntegerPartitions[n]; m[p_] := Max[Map[Length, Split[p]]] (* maximal multiplicity *)

%t Table[Count[f[n], p_ /; m[p] == Count[p, Min[p]]], {n, 0, z}] (* A240303 *)

%t Table[Count[f[n], p_ /; m[p] > Count[p, Min[p]]], {n, 0, z}] (* A240304 *)

%Y Cf. A240303, A000041, A171979.

%K nonn,easy

%O 0,8

%A _Clark Kimberling_, Apr 04 2014