A241067 - OEIS

%I #5 Apr 24 2014 10:28:30

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

%T 3,4,3,3,3,3,4,6,5,4,6,4,5,7,6,7,8,8,8,9,7,8,11,11,11,13,12,12,15,12,

%U 14,17,15,18,19,20,20

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

%e a(17) counts these 2 partitions:  {11,6}, {7,6,4}.

%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. A241065, A240874, A241068, A241036.

%K nonn,easy

%O 0,18

%A _Clark Kimberling_, Apr 16 2014