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Number of partitions p of n into distinct parts such that max(p) < -1 + 2*min(p).
3

%I #6 Apr 24 2014 10:28:21

%S 0,0,1,1,1,1,1,2,1,2,2,2,2,3,2,4,3,3,4,5,4,5,5,6,6,7,7,8,8,8,10,11,10,

%T 12,12,13,14,15,16,17,19,18,20,22,22,25,26,27,29,30,32,34,36,37,41,43,

%U 44,47,50,51,55,58,60,65,68,70,75,78,82,85,91

%N Number of partitions p of n into distinct parts such that max(p) < -1 + 2*min(p).

%e a(17) counts these 3 partitions: {17}, {10, 7}, {9,8}.

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

%t Table[Count[f[n], p_ /; Max[p] < -1 + 2*Min[p]], {n, 0, z}] (* A241065 *)

%t Table[Count[f[n], p_ /; Max[p] <= -1 + 2*Min[p]], {n, 0, z}] (* A240874 *)

%t Table[Count[f[n], p_ /; Max[p] == -1 + 2*Min[p]], {n, 0, z}] (* A241067 *)

%t Table[Count[f[n], p_ /; Max[p] >= -1 + 2*Min[p]], {n, 0, z}] (* A241068 *)

%t Table[Count[f[n], p_ /; Max[p] > -1 + 2*Min[p]], {n, 0, z}] (* A241036 *)

%Y Cf. A240874, A241067, A241068, A241036.

%K nonn,easy

%O 0,8

%A _Clark Kimberling_, Apr 16 2014