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A241318     Number of partitions p of n into distinct parts, including floor(mean(p)) and ceiling(mean(p)). 11
0, 1, 1, 2, 1, 2, 2, 2, 1, 4, 2, 3, 5, 3, 3, 9, 6, 5, 10, 7, 14, 15, 9, 12, 29, 23, 15, 27, 37, 26, 66, 30, 57, 51, 47, 104, 130, 63, 73, 99, 222, 110, 244, 129, 204, 316, 192, 222, 536, 376, 484, 340, 453, 421, 870, 808, 1121, 618, 680, 774, 2068, 951, 1076 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..62.

EXAMPLE

a(11) counts these 3 partitions:  {11}, {6,5}, {5321}.

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. A241319, A241320, A241321, A241322, A241312, A000009.

Sequence in context: A104640 A193335 A016727 * A276064 A054992 A096495

Adjacent sequences:  A241315 A241316 A241317 * A241319 A241320 A241321

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 19 2014

STATUS

approved

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Last modified March 28 20:44 EDT 2020. Contains 333103 sequences. (Running on oeis4.)