A238624 Number of partitions of n such that either both floor(n/2) and ceiling(n/2) are parts or else neither is a part.

0, 2, 2, 5, 4, 11, 9, 22, 20, 42, 40, 77, 77, 135, 141, 231, 247, 385, 420, 627, 696, 1002, 1124, 1575, 1782, 2436, 2776, 3718, 4256, 5604, 6437, 8349, 9617, 12310, 14203, 17977, 20764, 26015, 30070, 37338, 43166, 53174, 61469, 75175, 86879, 105558, 121926

Offset

1,2

Links

Table of n, a(n) for n=1..47.

Example

a(7) counts these 9 partitions:  7, 61, 52, 511, 43, 2221, 22111, 211111, 1111111.

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. A238622, A238623.

Sequence in context: A240412 A292263 A338528 * A124506 A264687 A112471

Adjacent sequences: A238621 A238622 A238623 * A238625 A238626 A238627

Keyword

nonn,easy

Author

Clark Kimberling, Mar 02 2014

Status

approved