OFFSET
0,3
COMMENTS
Here, "round(x)" is "Round[x]" in Mathematica: round(x) = the integer nearest x if x is not of the form k + 1/2, where k is an integer, and round(k + 1/2) = the even integer nearest k. (Thus round(3/2) "rounds up" to 2, whereas round(5/2) "rounds down" to 2.) For round(x) defined as floor(x + 1/2), see A241733.
EXAMPLE
a(6) counts these 8 partitions: 6, 33, 321, 3111, 222, 2211, 21111, 111111.
MATHEMATICA
z = 30; f[n_] := f[n] = IntegerPartitions[n];
Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]]], {n, 0, z}] (* A241334 *)
Table[Count[f[n], p_ /; ! MemberQ[p, Floor[Mean[p]]]], {n, 0, z}] (* A241335 *)
Table[Count[f[n], p_ /; MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241336 *)
Table[Count[f[n], p_ /; ! MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241337 *)
Table[Count[f[n], p_ /; MemberQ[p, Round[Mean[p]]]], {n, 0, z}] (* A241338 *)
Table[Count[f[n], p_ /; ! MemberQ[p, Round[Mean[p]]]], {n, 0, z}] (* A241339 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 20 2014
STATUS
approved