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A240209 Number of partitions p of n such that median(p) = multiplicity(max(p)). 5

%I #4 Apr 12 2014 16:23:39

%S 0,1,0,0,2,3,3,4,7,9,13,18,24,30,41,50,70,85,117,140,182,225,287,348,

%T 442,537,672,818,1010,1225,1509,1810,2208,2655,3210,3834,4629,5508,

%U 6605,7851,9364,11086,13188,15553,18422,21682,25568,29999,35285,41279,48378

%N Number of partitions p of n such that median(p) = multiplicity(max(p)).

%F a(n) = A240208(n) + A240207(n) for n >= 0.

%F a(n) + A240207(n) + A240210 = A000041(n) for n >= 0.

%e a(6) counts these 3 partitions: 411, 3111, 21111.

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

%t t1 = Table[Count[f[n], p_ /; Median[p] < Count[p, Max[p]]], {n, 0, z}] (* A240207 *)

%t t2 = Table[Count[f[n], p_ /; Median[p] <= Count[p, Max[p]]], {n, 0, z}] (* A240208 *)

%t t3 = Table[Count[f[n], p_ /; Median[p] == Count[p, Max[p]]], {n, 0, z}] (* A240209 *)

%t t4 = Table[Count[f[n], p_ /; Median[p] > Count[p, Max[p]]], {n, 0, z}] (* A240210 *)

%t t5 = Table[Count[f[n], p_ /; Median[p] >= Count[p, Max[p]]], {n, 0, z}] (* A240211 *)

%Y Cf. A240207, A240208, A240210, A240211, A000041.

%K nonn,easy

%O 0,5

%A _Clark Kimberling_, Apr 03 2014

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Last modified April 17 17:01 EDT 2024. Contains 371765 sequences. (Running on oeis4.)