A241317 Number of partitions p of n into distinct parts, including round(mean(p)).

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

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 * A357456 A185224 A001996

Adjacent sequences: A241314 A241315 A241316 * A241318 A241319 A241320

Keyword

nonn,easy

Author

Clark Kimberling, Apr 19 2014

Status

approved