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A296063
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a(n) is the smallest number (in absolute value) not yet in the sequence such that the arithmetic mean of the first n terms a(1), a(2), ..., a(n) is an integer. Preference is given to positive values of a(n); a(1)=1; 0 not allowed.
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3
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1, -1, 3, -3, 5, -5, 7, -7, 9, -9, 11, -11, 13, -13, 15, -15, 17, -17, 19, -19, 21, -21, 23, -23, 25, -25, 27, -27, 29, -29, 31, -31, 33, -33, 35, -35, 37, -37, 39, -39, 41, -41, 43, -43, 45, -45, 47, -47, 49, -49, 51, -51
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OFFSET
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1,3
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LINKS
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FORMULA
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G.f.: x*(1 + x^2) / ((1 - x)*(1 + x)^2).
a(n) = -a(n-1) + a(n-2) + a(n-3) for n>3.
(End)
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MATHEMATICA
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Array[(2 Floor[(# + 1)/2] - 1) (2 Boole@ OddQ@ # - 1) &, 52] (* or *)
Nest[Append[#, Block[{k = 1, s = 1}, While[Nand[FreeQ[#, s k], IntegerQ@ Mean[Append[#, s k]]], If[s == 1, s = -1, k++; s = 1]]; s k]] &, {1}, 51] (* Michael De Vlieger, Dec 12 2017 *)
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PROG
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(PARI) Vec(x*(1 + x^2) / ((1 - x)*(1 + x)^2) + O(x^50)) \\ Colin Barker, Mar 14 2020
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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