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 A241336 Number of partitions p of n including ceiling(mean(p)) as a part. 6
 0, 1, 2, 3, 4, 5, 7, 9, 12, 16, 22, 28, 39, 49, 66, 87, 112, 141, 190, 234, 307, 384, 482, 609, 783, 937, 1187, 1482, 1829, 2224, 2794, 3332, 4145, 5013, 6080, 7438, 9052, 10587, 12971, 15739, 18852, 22162, 26886, 31645, 38189, 45143, 52984, 63329, 75824 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..48. FORMULA a(n) + A241337(n) = A000041(n) for n >= 0. EXAMPLE a(6) counts these 7 partitions: 6, 33, 321, 222, 2211, 21111, 111111. MATHEMATICA z = 30; f[n_] := f[n] = IntegerPartitions[n]; Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]]], {n, 0, z}] (* A241334 *) Table[Count[f[n], p_ /; ! MemberQ[p, Floor[Mean[p]]]], {n, 0, z}] (* A241335 *) Table[Count[f[n], p_ /; MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241336 *) Table[Count[f[n], p_ /; ! MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241337 *) Table[Count[f[n], p_ /; MemberQ[p, Round[Mean[p]]]], {n, 0, z}] (* A241338 *) Table[Count[f[n], p_ /; ! MemberQ[p, Round[Mean[p]]]], {n, 0, z}] (* A241339 *) CROSSREFS Cf. A241334, A241335, A241337, A000041, A241312. Sequence in context: A117598 A120149 A117597 * A233522 A112639 A290137 Adjacent sequences: A241333 A241334 A241335 * A241337 A241338 A241339 KEYWORD nonn,easy AUTHOR Clark Kimberling, Apr 20 2014 STATUS approved

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Last modified June 8 18:04 EDT 2023. Contains 363165 sequences. (Running on oeis4.)