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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
OFFSET
1,4
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
Sequence in context: A058617 A205977 A363725 * A138135 A113166 A126872
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Mar 02 2014
STATUS
approved