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A240206 Number of partitions p of n such that mean(p) > multiplicity(min(p)). 5

%I #4 Apr 12 2014 16:23:17

%S 0,0,1,2,2,4,5,9,11,16,22,31,39,56,71,91,123,157,195,263,324,405,529,

%T 649,790,1032,1253,1514,1902,2357,2826,3497,4179,5153,6279,7459,8880,

%U 11079,13089,15435,18438,22596,26514,31423,36783,44336,52827,61570,71653

%N Number of partitions p of n such that mean(p) > multiplicity(min(p)).

%F a(n) = A240079(n) - A240205(n) for n >= 0.

%F a(n) + A240203(n) + A240205(n) = A000041(n) for n >= 0.

%e a(6) counts these 5 partitions: 6, 51, 42, 33, 321.

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

%t t1 = Table[Count[f[n], p_ /; Mean[p] < Count[p, Min[p]]], {n, 0, z}] (* A240203 *)

%t t2 = Table[Count[f[n], p_ /; Mean[p] <= Count[p, Min[p]]], {n, 0, z}] (* A240204 *)

%t t3 = Table[Count[f[n], p_ /; Mean[p] == Count[p, Min[p]]], {n, 0, z}] (* A240205 *)

%t t4 = Table[Count[f[n], p_ /; Mean[p] > Count[p, Min[p]]], {n, 0, z}] (* A240206 *)

%t t5 = Table[Count[f[n], p_ /; Mean[p] >= Count[p, Min[p]]], {n, 0, z}] (* A240079 *)

%Y Cf. A240203, A240204, A240205, A240079, A000041.

%K nonn,easy

%O 0,4

%A _Clark Kimberling_, Apr 03 2014

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Last modified March 4 22:06 EST 2024. Contains 370532 sequences. (Running on oeis4.)