|
%I #5 Apr 24 2014 10:28:38
%S 0,1,0,1,1,2,3,3,5,6,8,10,13,15,20,23,29,35,42,49,60,71,84,98,116,135,
%T 158,184,214,248,286,329,380,436,500,572,654,745,848,965,1094,1242,
%U 1406,1588,1794,2023,2278,2563,2881,3234,3626,4063,4546,5083,5677
%N Number of partitions p of n into distinct parts such that max(p) >= -1 + 2*min(p).
%e a(8) counts these 5 partitions: 71, 62, 53, 521, 431.
%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, A241067, A241036.
%K nonn,easy
%O 0,6
%A _Clark Kimberling_, Apr 16 2014
|
