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A241069 Number of partitions p of n into distinct parts such that max(p) = 4*min(p).

%I A241069 #7 May 11 2025 18:53:02
%S A241069 0,0,0,0,0,1,0,1,1,0,2,0,0,1,1,2,1,2,1,3,4,3,3,3,4,6,6,4,6,5,8,8,9,9,
%T A241069 10,13,11,13,15,17,20,21,21,24,25,29,30,33,35,40,44,44,49,51,56,61,66,
%U A241069 69,77,82,91,95,102,106,116,127,134,147,157,168,182
%N A241069 Number of partitions p of n into distinct parts such that max(p) = 4*min(p).
%e A241069 a(10) counts these 2 partitions:  82, 4321.
%t A241069 z = 40; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];
%t A241069     Table[Count[f[n], p_ /; Max[p] == 2*Min[p]], {n, 0, z}] (* A241035 *)
%t A241069     Table[Count[f[n], p_ /; Max[p] == 3*Min[p]], {n, 0, z}] (* A241063 *)
%t A241069     Table[Count[f[n], p_ /; Max[p] == 4*Min[p]], {n, 0, z}] (* A241069 *)
%t A241069     Table[Count[f[n], p_ /; Max[p] == 5*Min[p]], {n, 0, z}] (* A241272 *)
%t A241069     Table[Count[f[n], p_ /; Max[p] == 6*Min[p]], {n, 0, z}] (* A241273 *)
%Y A241069 Cf. A241035, A241063, A241272, A241273.
%K A241069 nonn,easy
%O A241069 0,11
%A A241069 _Clark Kimberling_, Apr 18 2014