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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.) 7
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 31 22:45 EDT 2020. Contains 334756 sequences. (Running on oeis4.)