|
%I #4 Apr 24 2014 10:29:07
%S 0,0,1,0,0,1,1,1,0,1,1,2,2,2,2,2,2,3,4,4,6,5,6,6,7,7,9,10,12,13,15,16,
%T 18,19,20,23,25,28,30,35,38,43,46,51,55,61,64,72,76,84,91,101,109,120,
%U 130,142,155,168,181,196,212,228,248,266,288,311,337
%N Number of partitions p of n into distinct parts such that max(p) = 2*(number of parts of p).
%e a(15) counts these 2 partitions: 8421, 654.
%t z = 40; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];
%t Table[Count[f[n], p_ /; Max[p] < 2*Length[p]], {n, 0, z}] (* A241085 *)
%t Table[Count[f[n], p_ /; Max[p] <= 2*Length[p]], {n, 0, z}] (* A241086 *)
%t Table[Count[f[n], p_ /; Max[p] == 2*Length[p]], {n, 0, z}] (* A241087 *)
%t Table[Count[f[n], p_ /; Max[p] >= 2*Length[p]], {n, 0, z}] (* A241088 *)
%t Table[Count[f[n], p_ /; Max[p] > 2*Length[p]], {n, 0, z}] (* A241089 *)
%Y Cf. A241085, A241086, A241088, A241089.
%K nonn,easy
%O 0,12
%A _Clark Kimberling_, Apr 17 2014
|
