A241315 Number of partitions p of n into distinct parts, not including ceiling(mean(p)).

0, 0, 0, 0, 1, 1, 2, 3, 4, 4, 7, 7, 10, 12, 15, 17, 23, 26, 32, 38, 45, 53, 65, 73, 87, 101, 120, 138, 160, 184, 211, 249, 285, 324, 373, 419, 487, 561, 633, 715, 808, 922, 1040, 1188, 1336, 1500, 1695, 1897, 2119, 2405, 2704, 3032, 3383, 3761, 4185, 4691

Offset

0,7

Links

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

Formula

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

Example

a(10) counts these 7 partitions:  91, 82, 73, 721, 64, 631, 532.

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, A241314, A241318, A000009.

Sequence in context: A167932 A006087 A364675 * A136330 A294267 A301763

Adjacent sequences: A241312 A241313 A241314 * A241316 A241317 A241318

Keyword

nonn,easy

Author

Clark Kimberling, Apr 19 2014

Status

approved