OFFSET
0,8
FORMULA
EXAMPLE
a(10) counts these 6 partitions: 91, 82, 721, 631, 541, 4321
MATHEMATICA
z = 70; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];
Table[Count[f[n], p_ /; Max[p] < 1 + 2*Min[p]], {n, 0, z}] (* A241061 *)
Table[Count[f[n], p_ /; Max[p] <= 1 + 2*Min[p]], {n, 0, z}] (* A207642 *)
Table[Count[f[n], p_ /; Max[p] == 1 + 2*Min[p]], {n, 0, z}] (* A241062 *)
Table[Count[f[n], p_ /; Max[p] >= 1 + 2*Min[p]], {n, 0, z}] (* A241037 *)
Table[Count[f[n], p_ /; Max[p] > 1 + 2*Min[p]], {n, 0, z}] (* A241064 *)
Table[Count[IntegerPartitions[n], _?(Length[#]==Length[Union[#]]&&#[[1]]>2#[[-1]]+1&)], {n, 0, 60}]//Quiet (* Harvey P. Dale, Sep 25 2024 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 16 2014
STATUS
approved