cp's OEIS Frontend

A240079 Number of partitions p of n such that mean(p) >= multiplicity(min(p)).

%I A240079 #4 Apr 06 2014 04:18:35
%S A240079 0,1,1,2,3,4,6,9,13,17,24,31,43,56,73,98,126,157,212,263,329,431,531,
%T A240079 649,850,1033,1255,1575,1961,2357,2917,3497,4328,5272,6281,7493,9360,
%U A240079 11079,13091,15650,19226,22596,26802,31423,37930,45259,52829,61570,74181
%N A240079 Number of partitions p of n such that mean(p) >= multiplicity(min(p)).
%F A240079 a(n) = A240206(n) - A240205(n) for n >= 0.
%F A240079 a(n) + A240203(n) = A000041(n) for n >= 0.
%e A240079 a(6) counts these 5 partitions:  6, 51, 42, 33, 321.
%t A240079 z = 60; f[n_] := f[n] = IntegerPartitions[n];
%t A240079 t1 = Table[Count[f[n], p_ /; Mean[p] < Count[p, Min[p]]], {n, 0, z}]  (* A240203 *)
%t A240079 t2 = Table[Count[f[n], p_ /; Mean[p] <= Count[p, Min[p]]], {n, 0, z}] (* A240204 *)
%t A240079 t3 = Table[Count[f[n], p_ /; Mean[p] == Count[p, Min[p]]], {n, 0, z}] (* A240205 *)
%t A240079 t4 = Table[Count[f[n], p_ /; Mean[p] > Count[p, Min[p]]], {n, 0, z}] (* A240206 *)
%t A240079 t5 = Table[Count[f[n], p_ /; Mean[p] >= Count[p, Min[p]]], {n, 0, z}] (* A240079 *)
%Y A240079 Cf. A240203, A240204, A240205, A240206, A000041.
%K A240079 nonn,easy
%O A240079 0,4
%A A240079 _Clark Kimberling_, Apr 03 2014