A241313 Number of partitions p of n into distinct parts, not including floor(mean(p)).

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

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.

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, A241314, A241315, A241318, A000009.

Sequence in context: A240844 A136343 A161254 * A241317 A357456 A185224

Adjacent sequences: A241310 A241311 A241312 * A241314 A241315 A241316

Keyword

nonn,easy

Author

Clark Kimberling, Apr 19 2014

Status

approved