A241318 Number of partitions p of n into distinct parts, including floor(mean(p)) and ceiling(mean(p)).

0, 1, 1, 2, 1, 2, 2, 2, 1, 4, 2, 3, 5, 3, 3, 9, 6, 5, 10, 7, 14, 15, 9, 12, 29, 23, 15, 27, 37, 26, 66, 30, 57, 51, 47, 104, 130, 63, 73, 99, 222, 110, 244, 129, 204, 316, 192, 222, 536, 376, 484, 340, 453, 421, 870, 808, 1121, 618, 680, 774, 2068, 951, 1076

Offset

0,4

Links

Table of n, a(n) for n=0..62.

Example

a(11) counts these 3 partitions:  {11}, {6,5}, {5321}.

Mathematica

z = 30; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];
    Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]] && MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241318 *)
    Table[Count[f[n], p_ /; ! MemberQ[p, Floor[Mean[p]]] && MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241319 *)
    Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]] && ! MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241320 *)
    Table[Count[f[n], p_ /; ! MemberQ[p, Floor[Mean[p]]] && ! MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241321 *)
    Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]] || MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241322 *)

Crossrefs

Cf. A241319, A241320, A241321, A241322, A241312, A000009.

Sequence in context: A193335 A016727 A335420 * A276064 A054992 A096495

Adjacent sequences: A241315 A241316 A241317 * A241319 A241320 A241321

Keyword

nonn,easy

Author

Clark Kimberling, Apr 19 2014

Status

approved