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A241334
Number of partitions p of n including floor(mean(p)) as a part.
6
0, 1, 2, 3, 4, 6, 8, 11, 15, 21, 27, 38, 48, 65, 86, 111, 140, 189, 233, 306, 383, 481, 608, 782, 936, 1186, 1481, 1828, 2223, 2793, 3331, 4144, 5012, 6079, 7437, 9051, 10586, 12970, 15738, 18851, 22161, 26885, 31644, 38188, 45142, 52983, 63328, 75823, 87404
OFFSET
0,3
FORMULA
a(n) + A241335(n) = A000041(n) for n >= 0.
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