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%I A240178 #6 Apr 12 2014 16:21:10
%S A240178 0,0,1,1,1,2,3,4,5,7,9,13,16,22,27,36,44,59,71,93,114,144,176,223,268,
%T A240178 336,407,502,605,744,891,1088,1301,1574,1879,2265,2687,3224,3822,4557,
%U A240178 5384,6399,7535,8921,10481,12354,14481,17022,19888,23307,27178,31745
%N A240178 Number of partitions of n such that (least part) < (multiplicity of greatest part).
%C A240178 For n >=1, a(n) is also the number of partitions of n such that (least part) > (multiplicity of greatest part), as well as the number of partitions p of n such that min(p) < min(c(p)), where c = conjugate.
%F A240178 a(n) = A240179(n) - A240180(n), for n >= 0.
%e A240178 a(6) counts these 3 partitions:  222, 2211, 111111.
%t A240178 z = 60; f[n_] := f[n] = IntegerPartitions[n]; Table[Count[f[n], p_ /; Min[p] < Count[p, Max[p]]], {n, 0, z}]  (* A240178 *)
%t A240178 Table[Count[f[n], p_ /; Min[p] <= Count[p, Max[p]]], {n, 0, z}] (* A240179 *)
%t A240178 Table[Count[f[n], p_ /; Min[p] == Count[p, Max[p]]], {n, 0, z}] (* A240180 *)
%t A240178 Table[Count[f[n], p_ /; Min[p] > Count[p, Max[p]]], {n, 0, z}]  (* A240178, n>0 *)
%t A240178 Table[Count[f[n], p_ /; Min[p] >= Count[p, Max[p]]], {n, 0, z}] (* A240179, n>0 *)
%Y A240178 Cf. A240179, A240180.
%K A240178 nonn,easy
%O A240178 0,6
%A A240178 _Clark Kimberling_, Apr 02 2014

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