A241339 Number of partitions p of n not including round(mean(p)) as a part. (This is "Mathematica round"; for round(x) defined as floor(x + 1/2), see A241734.)

1, 0, 0, 0, 1, 2, 4, 5, 9, 12, 17, 25, 33, 44, 62, 77, 104, 131, 180, 222, 278, 368, 454, 581, 717, 883, 1112, 1345, 1745, 2093, 2519, 3068, 3820, 4688, 5570, 6744, 8151, 9738, 11716, 14199, 16723, 20210, 24151, 28582, 33728, 39373, 48163, 55979, 65738

Offset

0,6

Comments

Here, "round(x)" is "Round[x]" in Mathematica: round(x) = the integer nearest x if x is not of the form k + 1/2, where k is an integer, and round(k + 1/2) = the even integer nearest k. (Thus round(3/2) "rounds up" to 2, whereas round(5/2) "rounds down" to 2.)

Links

Table of n, a(n) for n=0..48.

Formula

a(n) + A241338(n) = A000041(n) for n >= 0.

Example

a(6) counts these 4 partitions:  51, 42, 411, 3111.

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

Cf. A241334, A241338, A000041, A241312, A241734.

Sequence in context: A087667 A241444 A082592 * A327781 A241411 A211373

Adjacent sequences: A241336 A241337 A241338 * A241340 A241341 A241342

Keyword

nonn,easy

Author

Clark Kimberling, Apr 20 2014

Status

approved