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A241316     Number of partitions p of n into distinct parts, including round(mean(p)). 6
0, 1, 1, 2, 1, 2, 2, 3, 2, 4, 4, 5, 5, 7, 7, 10, 10, 13, 15, 17, 19, 25, 27, 31, 35, 44, 49, 59, 63, 74, 85, 99, 114, 126, 143, 166, 189, 221, 242, 277, 306, 351, 404, 447, 506, 565, 623, 710, 791, 899, 1021, 1150, 1268, 1364, 1533, 1734, 1949, 2149, 2386 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..58.

FORMULA

a(n) + A241317(n) = A000009(n) for n >= 1.

EXAMPLE

a(10) counts these 4 partitions:  {10,}, {5,4,1}, {5,3,2}, {4,3,2,1}.

MATHEMATICA

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

    Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]]], {n, 0, z}] (* A241312 *)

    Table[Count[f[n], p_ /; ! MemberQ[p, Floor[Mean[p]]]], {n, 0, z}] (* A241313 *)

    Table[Count[f[n], p_ /; MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241314 *)

    Table[Count[f[n], p_ /; ! MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241315 *)

    Table[Count[f[n], p_ /; MemberQ[p, Round[Mean[p]]]], {n, 0, z}] (* A241316 *)

    Table[Count[f[n], p_ /; ! MemberQ[p, Round[Mean[p]]]], {n, 0, ] (* A241317 *)

CROSSREFS

Cf. A241317, A241318, A000009.

Sequence in context: A127685 A127687 A024156 * A241312 A075989 A304714

Adjacent sequences:  A241313 A241314 A241315 * A241317 A241318 A241319

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 19 2014

STATUS

approved

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Last modified April 5 10:20 EDT 2020. Contains 333239 sequences. (Running on oeis4.)