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A238623 Number of partitions of n such that neither floor(n/2) nor ceiling(n/2) is a part. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A135291 A058617 A205977 * A138135 A113166 A126872

Adjacent sequences:  A238620 A238621 A238622 * A238624 A238625 A238626

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Mar 02 2014

STATUS

approved

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Last modified June 4 03:40 EDT 2020. Contains 334815 sequences. (Running on oeis4.)