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A241314
Number of partitions p of n into distinct parts, including ceiling(mean(p)).
6
0, 1, 1, 2, 1, 2, 2, 2, 2, 4, 3, 5, 5, 6, 7, 10, 9, 12, 14, 16, 19, 23, 24, 31, 35, 41, 45, 54, 62, 72, 85, 91, 105, 124, 139, 166, 181, 199, 231, 267, 305, 338, 386, 422, 480, 548, 609, 693, 791, 859, 954, 1065, 1199, 1359, 1533, 1687, 1873, 2025, 2281
OFFSET
0,4
FORMULA
a(n) + A241314(n) = A000009(n) for n >= 1.
EXAMPLE
a(10) counts these 3 partitions: {10,}, {5,4,1}, {5,4,2,1}.
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