A238623 Number of partitions of n such that neither floor(n/2) nor ceiling(n/2) is a part.

0, 1, 1, 3, 3, 8, 8, 17, 19, 35, 39, 66, 76, 120, 140, 209, 246, 355, 419, 585, 695, 946, 1123, 1498, 1781, 2335, 2775, 3583, 4255, 5428, 6436, 8118, 9616, 12013, 14202, 17592, 20763, 25525, 30069, 36711, 43165, 52382, 61468, 74173, 86878, 104303, 121925

Offset

1,4

Links

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

Formula

a(n) + A238622(n) = A000041(n).

Example

a(7) counts these 8 partitions:  7, 61, 52, 511, 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, A238624.

Sequence in context: A058617 A205977 A363725 * A138135 A113166 A126872

Adjacent sequences: A238620 A238621 A238622 * A238624 A238625 A238626

Keyword

nonn,easy

Author

Clark Kimberling, Mar 02 2014

Status

approved