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A241341 Number of partitions p of n such that ceiling(mean(p)) is a part and floor(mean(p)) is not. 5
0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 4, 6, 2, 13, 16, 14, 23, 41, 38, 73, 58, 94, 152, 196, 137, 271, 384, 422, 481, 751, 624, 1149, 1142, 1558, 2096, 2120, 2116, 3748, 4477, 5075, 4788, 7840, 7543, 11227, 11772, 13122, 18916, 22408, 19619, 29862, 32604, 41688 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,11

LINKS

Table of n, a(n) for n=0..51.

EXAMPLE

a(10) counts these 4 partitions:  541, 5311, 442, 3331.

MATHEMATICA

z = 30; f[n_] := f[n] = IntegerPartitions[n];

    t1 = Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]] && MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241340 *)

    t2 = Table[Count[f[n], p_ /; ! MemberQ[p, Floor[Mean[p]]] && MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241341 *)

    t3 = Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]] && ! MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241342 *)

    t4 = Table[Count[f[n], p_ /; ! MemberQ[p, Floor[Mean[p]]] && ! MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241343 *)

    t5 = Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]] || MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241344 *)

CROSSREFS

Cf. A241340, A241342, A241343, A241344.

Sequence in context: A256508 A059030 A066984 * A085595 A173458 A054222

Adjacent sequences:  A241338 A241339 A241340 * A241342 A241343 A241344

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 20 2014

STATUS

approved

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Last modified May 31 06:52 EDT 2020. Contains 334747 sequences. (Running on oeis4.)