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A241734
Number of partitions p of n such that round(mean(p)) is not a part of p; here, round(x) means floor(x + 1/2).
3
1, 0, 0, 0, 1, 2, 4, 5, 9, 12, 18, 25, 33, 44, 62, 82, 104, 131, 182, 222, 289, 368, 454, 581, 717, 912, 1115, 1367, 1745, 2093, 2578, 3068, 3820, 4688, 5574, 6870, 8278, 9738, 11716, 14259, 16961, 20210, 24156, 28582, 33728, 40446, 48163, 55979, 657385
OFFSET
0,6
COMMENTS
For the corresponding sequence using "round" as in Mathematica, see A241339.
FORMULA
a(n) + A241733(n) = A000041(n) for n >= 0.
EXAMPLE
a(6) counts these 4 partitions: 51, 42, 411, 3111.
MATHEMATICA
z = 40; f[n_] := f[n] = IntegerPartitions[n];
Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p] + 1/2]]], {n, 0, z}] (* A241733 *)
Table[Count[f[n], p_ /; ! MemberQ[p, Floor[Mean[p] + 1/2]]], {n, 0, z}] (* A241734 *)
CROSSREFS
Sequence in context: A327781 A241411 A211373 * A371171 A039898 A083690
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 28 2014
STATUS
approved