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A238622 Number of partitions of n such that floor(n/2) or ceiling(n/2) is a part. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A286931 A265701 A007439 * A096441 A100824 A163227

Adjacent sequences:  A238619 A238620 A238621 * A238623 A238624 A238625

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Mar 02 2014

STATUS

approved

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Last modified February 16 02:32 EST 2019. Contains 320140 sequences. (Running on oeis4.)