cp's OEIS Frontend

A241062 Number of partitions p of n into distinct parts such that max(p) = 1 + 2*min(p).

%I A241062 #9 Apr 22 2014 22:18:07
%S A241062 0,0,0,0,1,0,1,1,0,0,2,1,0,1,2,1,2,0,1,3,2,2,2,1,2,4,4,2,3,2,3,6,4,4,
%T A241062 6,4,4,5,6,8,8,7,6,8,7,8,12,10,10,13,12,11,12,12,14,18,18,17,18,18,18,
%U A241062 22,20,22,26,25,28,30,29,30,32
%N A241062 Number of partitions p of n into distinct parts such that max(p) = 1 + 2*min(p).
%F A241062     a(n) + A241061(n) + A241064(n) = A000009(n) for n >= 1.
%F A241062     a(n) = A241037(n) - A241064(n) = A207642(n) - A241061(n) for n >= 0.
%e A241062 a(10) counts these 2 partitions:  73, 532.
%t A241062 z = 70; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];
%t A241062   Table[Count[f[n], p_ /; Max[p] < 1 + 2*Min[p]], {n, 0, z}] (* A241061 *)
%t A241062   Table[Count[f[n], p_ /; Max[p] <= 1 + 2*Min[p]], {n, 0, z}](* A207642 *)
%t A241062   Table[Count[f[n], p_ /; Max[p] == 1 + 2*Min[p]], {n, 0, z}](* A241062 *)
%t A241062   Table[Count[f[n], p_ /; Max[p] >= 1 + 2*Min[p]], {n, 0, z}](* A241037 *)
%t A241062   Table[Count[f[n], p_ /; Max[p] > 1 + 2*Min[p]], {n, 0, z}] (* A241064 *)
%Y A241062 Cf. A207642, A241061, A241037, A241064, A000009.
%K A241062 nonn,easy
%O A241062 0,11
%A A241062 _Clark Kimberling_, Apr 16 2014