OFFSET
0,6
FORMULA
a(15) counts these 7 partitions: 8421, 7521, 7431, 654, 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