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Number of partitions p of n into distinct parts such that max(p) = 2*min(p).
10

%I #11 Jan 05 2019 04:36:58

%S 0,0,0,1,0,0,1,0,0,2,0,0,1,1,1,1,0,1,3,1,0,2,1,2,3,2,1,2,2,3,5,2,2,4,

%T 3,3,5,5,5,6,3,4,7,6,7,9,7,6,9,8,8,10,10,12,14,11,11,13,13,14,17,16,

%U 17,21,18,19,22,20,21,25,25

%N Number of partitions p of n into distinct parts such that max(p) = 2*min(p).

%e a(9) counts these 2 partitions: {6,3}, {4,3,2}.

%t z = 70; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];

%t Table[Count[f[n], p_ /; Max[p] < 2*Min[p]], {n, 0, z}] (* A240874 *)

%t Table[Count[f[n], p_ /; Max[p] == 2*Min[p]], {n, 0, z}] (* A241035 *)

%t Table[Count[f[n], p_ /; Max[p] >= 2*Min[p]], {n, 0, z}] (* A241036 *)

%t Table[Count[f[n], p_ /; Max[p] > 2*Min[p]], {n, 0, z}] (* A241037 *)

%Y Cf. A240874, A241036, A241037.

%K nonn,easy

%O 0,10

%A _Clark Kimberling_, Apr 15 2014