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A241319 Number of partitions p of n into distinct parts, including ceiling(mean(p)) but not floor(mean(p)). 5
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 0, 3, 4, 1, 3, 7, 4, 9, 5, 8, 15, 19, 6, 18, 30, 27, 25, 46, 19, 61, 48, 73, 92, 62, 51, 136, 158, 168, 83, 228, 142, 293, 276, 232, 417, 471, 255, 483, 470, 725, 746, 938, 663, 879, 752, 1407, 1601, 1789, 814, 2172, 2431 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,12

LINKS

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

EXAMPLE

a(11) counts these 2 partitions:  731, 632.

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, A241320, A241321, A241322, A000009.

Sequence in context: A137372 A212844 A066439 * A287016 A285722 A274441

Adjacent sequences:  A241316 A241317 A241318 * A241320 A241321 A241322

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 19 2014

STATUS

approved

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Last modified April 6 08:44 EDT 2020. Contains 333268 sequences. (Running on oeis4.)