A241061 - OEIS

%I #13 Nov 09 2024 02:29:05

%S 0,1,1,2,1,2,2,2,2,4,2,3,4,4,4,5,4,6,7,6,6,8,8,9,10,10,10,12,12,14,16,

%T 14,16,18,18,20,22,23,24,26,26,28,32,32,35,38,38,40,44,45,48,52,54,58,

%U 62,62,66,71,74,78,84,86,92,98,100,106,112,116,122

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

%F     a(n) + A241062(n) + A241064(n) = A000009(n) for n >= 1.

%F     a(n) = A207642(n) - A241062(n) for n >= 0.

%e a(10) counts these 2 partitions: {10}, {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}] (* A241061 *)

%t   Table[Count[f[n], p_ /; Max[p] <= 1 + 2*Min[p]], {n, 0, z}](* A207642 *)

%t   Table[Count[f[n], p_ /; Max[p] == 1 + 2*Min[p]], {n, 0, z}](* A241062 *)

%t   Table[Count[f[n], p_ /; Max[p] >= 1 + 2*Min[p]], {n, 0, z}](* A241037 *)

%t   Table[Count[f[n], p_ /; Max[p] > 1 + 2*Min[p]], {n, 0, z}] (* A241064 *)

%Y Cf. A207642, A241062, A241037, A241064, A000009.

%K nonn,easy

%O 0,4

%A _Clark Kimberling_, Apr 16 2014