cp's OEIS Frontend

A240182 Number of partitions of n such that (greatest part) <= (multiplicity of least part).

%I A240182 #9 Apr 12 2014 16:21:52
%S A240182 1,1,1,1,3,2,5,4,8,10,13,15,25,25,37,46,61,70,97,112,150,177,224,270,
%T A240182 347,407,508,611,754,895,1106,1304,1594,1892,2283,2708,3262,3835,4595,
%U A240182 5421,6452,7574,8993,10530,12445,14564,17123,19992,23465,27302,31931
%N A240182 Number of partitions of n such that (greatest part) <= (multiplicity of least part).
%F A240182 a(n) = A240178(n) + A240183(n), for n >= 1.
%F A240182 a(n) + A240179(n) = A000041(n) for n >= 0.
%e A240182 a(8) counts these 8 partitions:  41111, 32111, 311111, 2222, 22211, 221111, 2111111, 11111111.
%t A240182 z = 60; f[n_] := f[n] = IntegerPartitions[n];
%t A240182 t1 = Table[Count[f[n], p_ /; Max[p] < Count[p, Min[p]]], {n, 0, z}]  (* A240178 except for n=0 *)
%t A240182 t2 = Table[Count[f[n], p_ /; Max[p] <= Count[p, Min[p]]], {n, 0, z}] (* A240182 *)
%t A240182 t3 = Table[Count[f[n], p_ /; Max[p] == Count[p, Min[p]]], {n, 0, z}] (* A240183 *)
%t A240182 t4 = Table[Count[f[n], p_ /; Max[p] > Count[p, Min[p]]], {n, 0, z}] (* A240184 *)
%t A240182 t5 = Table[Count[f[n], p_ /; Max[p] >= Count[p, Min[p]]], {n, 0, z}] (* A240179 *)
%Y A240182 Cf. A240178, A240183, A240184, A240179, A000041.
%K A240182 nonn,easy
%O A240182 0,5
%A A240182 _Clark Kimberling_, Apr 02 2014