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A241733
Number of partitions p of n such that round(mean(p)) is a part of p; here, round(x) means floor(x + 1/2).
3
0, 1, 2, 3, 4, 5, 7, 10, 13, 18, 24, 31, 44, 57, 73, 94, 127, 166, 203, 268, 338, 424, 548, 674, 858, 1046, 1321, 1643, 1973, 2472, 3026, 3774, 4529, 5455, 6736, 8013, 9699, 11899, 14299, 16926, 20377, 24373, 29018, 34679, 41447, 48688, 57395, 68775, 81535
OFFSET
0,3
COMMENTS
For the corresponding sequence using "round" as in Mathematica, see A241338.
FORMULA
a(n) + A241734(n) = A000041(n) for n >= 0.
EXAMPLE
a(6) counts these 7 partitions: 6, 33, 321, 222, 2211, 21111, 111111.
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: A193771 A160333 A174578 * A241338 A271489 A018127
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 28 2014
STATUS
approved