A238622 Number of partitions of n such that floor(n/2) or ceiling(n/2) is a part.

1, 1, 2, 2, 4, 3, 7, 5, 11, 7, 17, 11, 25, 15, 36, 22, 51, 30, 71, 42, 97, 56, 132, 77, 177, 101, 235, 135, 310, 176, 406, 231, 527, 297, 681, 385, 874, 490, 1116, 627, 1418, 792, 1793, 1002, 2256, 1255, 2829, 1575, 3532, 1958, 4393, 2436, 5445, 3010, 6727

Offset

1,3

Links

Table of n, a(n) for n=1..55.

Formula

a(n) + A238623(n) = A000041(n).

Example

a(7) counts these partitions:  43, 421, 4111, 331, 322, 3211, 31111.

Mathematica

z=40; g[n_] := g[n] = IntegerPartitions[n];
t1 = Table[Count[g[n], p_ /; Or[MemberQ[p, Floor[n/2]], MemberQ[p, Ceiling[n/2]]]], {n, z}]   (* A238622 [or] *)
t2 = Table[Count[g[n], p_ /; Nor[MemberQ[p, Floor[n/2]], MemberQ[p, Ceiling[n/2]]]], {n, z}]   (* A238623 [nor] *)
t3 = Table[Count[g[n], p_ /; Xnor[MemberQ[p, Floor[n/2]], MemberQ[p, Ceiling[n/2]]]], {n, z}]   (* A238624 [xnor] *)

Crossrefs

Cf. A238623, A238624.

Sequence in context: A265701 A353747 A007439 * A096441 A100824 A163227

Adjacent sequences: A238619 A238620 A238621 * A238623 A238624 A238625

Keyword

nonn,easy

Author

Clark Kimberling, Mar 02 2014

Status

approved