cp's OEIS Frontend

A241064 Number of partitions p of n into distinct parts such that max(p) > 1 + 2*min(p).

%I A241064 #10 Sep 25 2024 12:08:36
%S A241064 0,0,0,0,0,1,1,2,4,4,6,8,11,13,16,21,26,32,38,45,56,66,79,94,110,128,
%T A241064 151,178,207,240,277,320,370,426,488,561,642,732,834,948,1079,1225,
%U A241064 1388,1570,1774,2002,2254,2540,2856,3206,3598,4034,4516,5050,5642,6298
%N A241064 Number of partitions p of n into distinct parts such that max(p) > 1 + 2*min(p).
%F A241064     a(n) + A241061(n) + A241062(n) = A000009(n) for n >= 1.
%F A241064     a(n) = A241037(n) - A241062(n) for n>= 0.
%e A241064 a(10) counts these 6 partitions:  91, 82, 721, 631, 541, 4321
%t A241064 z = 70; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];
%t A241064 Table[Count[f[n], p_ /; Max[p] < 1 + 2*Min[p]], {n, 0, z}]  (* A241061 *)
%t A241064 Table[Count[f[n], p_ /; Max[p] <= 1 + 2*Min[p]], {n, 0, z}] (* A207642 *)
%t A241064 Table[Count[f[n], p_ /; Max[p] == 1 + 2*Min[p]], {n, 0, z}] (* A241062 *)
%t A241064 Table[Count[f[n], p_ /; Max[p] >= 1 + 2*Min[p]], {n, 0, z}] (* A241037 *)
%t A241064 Table[Count[f[n], p_ /; Max[p] > 1 + 2*Min[p]], {n, 0, z}]  (* A241064 *)
%t A241064 Table[Count[IntegerPartitions[n],_?(Length[#]==Length[Union[#]]&&#[[1]]>2#[[-1]]+1&)],{n,0,60}]//Quiet (* _Harvey P. Dale_, Sep 25 2024 *)
%Y A241064 Cf. A207642, A241061, A241062, A241064, A000009.
%K A241064 nonn,easy
%O A241064 0,8
%A A241064 _Clark Kimberling_, Apr 16 2014