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A241317 Number of partitions p of n into distinct parts, including round(mean(p)). 6
0, 0, 0, 0, 1, 1, 2, 2, 4, 4, 6, 7, 10, 11, 15, 17, 22, 25, 31, 37, 45, 51, 62, 73, 87, 98, 116, 133, 159, 182, 211, 241, 276, 322, 369, 419, 479, 539, 622, 705, 807, 909, 1022, 1163, 1310, 1483, 1681, 1880, 2119, 2365, 2637, 2947, 3314, 3756, 4185, 4644 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

LINKS

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

FORMULA

a(n) + A241316(n) = A000009(n) for n >= 1.

EXAMPLE

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

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. A241316, A241318, A000009.

Sequence in context: A136343 A161254 A241313 * A185224 A001996 A317084

Adjacent sequences:  A241314 A241315 A241316 * A241318 A241319 A241320

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 19 2014

STATUS

approved

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Last modified February 27 09:59 EST 2020. Contains 332304 sequences. (Running on oeis4.)