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A241313     Number of partitions p of n into distinct parts, not including floor(mean(p)). 6
0, 0, 0, 0, 1, 1, 2, 2, 4, 4, 6, 7, 10, 11, 15, 16, 22, 25, 31, 35, 45, 51, 61, 70, 85, 98, 116, 131, 156, 176, 209, 238, 276, 314, 356, 411, 479, 539, 612, 688, 792, 891, 1022, 1149, 1295, 1462, 1641, 1831, 2088, 2346, 2637, 2941, 3277, 3648, 4097, 4575 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

LINKS

Table of n, a(n) for n=0..55.

FORMULA

a(n) + A241312(n) = A000009(n) for n >= 1.

EXAMPLE

    a(10) counts these 6 partitions:  91, 82, 73, 721, 64, 631.

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

MATHEMATICA

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, A241314, A241315, A241318, A000009.

Sequence in context: A240844 A136343 A161254 * A241317 A185224 A001996

Adjacent sequences:  A241310 A241311 A241312 * A241314 A241315 A241316

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 19 2014

STATUS

approved

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Last modified August 12 04:57 EDT 2020. Contains 336436 sequences. (Running on oeis4.)