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A241314     Number of partitions p of n into distinct parts, including ceiling(mean(p)). 6
0, 1, 1, 2, 1, 2, 2, 2, 2, 4, 3, 5, 5, 6, 7, 10, 9, 12, 14, 16, 19, 23, 24, 31, 35, 41, 45, 54, 62, 72, 85, 91, 105, 124, 139, 166, 181, 199, 231, 267, 305, 338, 386, 422, 480, 548, 609, 693, 791, 859, 954, 1065, 1199, 1359, 1533, 1687, 1873, 2025, 2281 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

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

FORMULA

a(n) + A241314(n) = A000009(n) for n >= 1.

EXAMPLE

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

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. A241312, A241313, A241315, A241318, A000009.

Sequence in context: A277210 A304777 A058762 * A276056 A276060 A276058

Adjacent sequences:  A241311 A241312 A241313 * A241315 A241316 A241317

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 19 2014

STATUS

approved

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Last modified October 16 14:35 EDT 2018. Contains 316263 sequences. (Running on oeis4.)