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A241085
Number of partitions p of n into distinct parts such that max(p) < 2*(number of parts of p).
5
0, 1, 0, 1, 1, 1, 1, 1, 2, 2, 3, 2, 3, 3, 4, 5, 6, 6, 7, 8, 8, 10, 11, 13, 14, 17, 18, 21, 22, 25, 27, 31, 33, 38, 42, 47, 52, 57, 63, 69, 76, 82, 91, 99, 109, 119, 132, 142, 158, 171, 188, 203, 223, 240, 263, 284, 309, 334, 364, 393, 428, 463, 501, 543, 588
OFFSET
0,9
EXAMPLE
a(15) counts these 5 partitions: 7521, 7431, 6531, 6432, 54321.
MATHEMATICA
z = 40; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];
Table[Count[f[n], p_ /; Max[p] < 2*Length[p]], {n, 0, z}] (* A241085 *)
Table[Count[f[n], p_ /; Max[p] <= 2*Length[p]], {n, 0, z}] (* A241086 *)
Table[Count[f[n], p_ /; Max[p] == 2*Length[p]], {n, 0, z}] (* A241087 *)
Table[Count[f[n], p_ /; Max[p] >= 2*Length[p]], {n, 0, z}] (* A241088 *)
Table[Count[f[n], p_ /; Max[p] > 2*Length[p]], {n, 0, z}] (* A241089 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 17 2014
STATUS
approved