OFFSET
0,7
EXAMPLE
a(10) counts these 6 partitions: 91, 82, 73, 721, 64, 631.
MATHEMATICA
z = 30;
f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];
Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]]], {n, 0, z}] (* A241312 *)
Table[Count[f[n], p_ /; ! MemberQ[p, Floor[Mean[p]]]], {n, 0, z}] (* A241313 *)
Table[Count[f[n], p_ /; MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241314 *)
Table[Count[f[n], p_ /; ! MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241315 *)
Table[Count[f[n], p_ /; MemberQ[p, Round[Mean[p]]]], {n, 0, z}] (* A241316 *)
Table[Count[f[n], p_ /; ! MemberQ[p, Round[Mean[p]]]], {n, 0, ] (* A241317 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 19 2014
STATUS
approved