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A241312
Number of partitions p of n into distinct parts, including floor(mean(p)).
16
0, 1, 1, 2, 1, 2, 2, 3, 2, 4, 4, 5, 5, 7, 7, 11, 10, 13, 15, 19, 19, 25, 28, 34, 37, 44, 49, 61, 66, 80, 87, 102, 114, 134, 156, 174, 189, 221, 252, 294, 321, 369, 404, 461, 521, 586, 663, 759, 822, 918, 1021, 1156, 1305, 1472, 1621, 1803, 1949, 2202, 2469
OFFSET
0,4
FORMULA
a(n) + A241313(n) = A000009(n) for n >= 1.
EXAMPLE
a(10) counts these 4 partitions: {10}, {5,4,1}, {5,3,2}, {4,3,2,1}.
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