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A241320 Number of partitions p of n into distinct parts, including floor(mean(p)) but not ceiling(mean(p)). 5
0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 4, 4, 2, 4, 8, 5, 12, 5, 10, 19, 22, 8, 21, 34, 34, 29, 54, 21, 72, 57, 83, 109, 70, 59, 158, 179, 195, 99, 259, 160, 332, 317, 270, 471, 537, 286, 542, 537, 816, 852, 1051, 751, 995, 828, 1584, 1789, 2005, 941, 2431 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,11

LINKS

Table of n, a(n) for n=0..61.

EXAMPLE

a(11) counts these 2 partitions:  641, 542.

MATHEMATICA

z = 30; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];

    Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]] && MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241318 *)

    Table[Count[f[n], p_ /; ! MemberQ[p, Floor[Mean[p]]] && MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241319 *)

    Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]] && ! MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241320 *)

    Table[Count[f[n], p_ /; ! MemberQ[p, Floor[Mean[p]]] && ! MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241321 *)

    Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]] || MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241322 *)

CROSSREFS

Cf. A241318, A241319, A241321, A241322, A241312, A000009.

Sequence in context: A078030 A262056 A264628 * A073469 A307076 A308720

Adjacent sequences:  A241317 A241318 A241319 * A241321 A241322 A241323

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 19 2014

STATUS

approved

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Last modified March 29 05:39 EDT 2020. Contains 333105 sequences. (Running on oeis4.)