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 A241338 Number of partitions p of n including round(mean(p)) as a part.  (This is "Mathematica round") 8
 0, 1, 2, 3, 4, 5, 7, 10, 13, 18, 25, 31, 44, 57, 73, 99, 127, 166, 205, 268, 349, 424, 548, 674, 858, 1075, 1324, 1665, 1973, 2472, 3085, 3774, 4529, 5455, 6740, 8139, 9826, 11899, 14299, 16986, 20615, 24373, 29023, 34679, 41447, 49761, 57395, 68775, 81535 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Here, "round(x)" is "Round[x]" in Mathematica:  round(x) = the integer nearest x if x is not of the form k + 1/2, where k is an integer, and round(k + 1/2) = the even integer nearest k.  (Thus round(3/2) "rounds up" to 2, whereas round(5/2) "rounds down" to 2.) For round(x) defined as floor(x + 1/2), see A241733. LINKS FORMULA a(n) + A241339(n) = A000041(n) for n >= 0. EXAMPLE a(6) counts these 8 partitions:  6, 33, 321, 3111, 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, A241339, A000041, A241312, A241733. Sequence in context: A160333 A174578 A241733 * A271489 A018127 A017835 Adjacent sequences:  A241335 A241336 A241337 * A241339 A241340 A241341 KEYWORD nonn,easy AUTHOR Clark Kimberling, Apr 20 2014 STATUS approved

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Last modified October 1 04:06 EDT 2020. Contains 337441 sequences. (Running on oeis4.)