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A012265
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x - x^3/3! + x^5/5! - ... + (-1)^n*x^(2n+1)/(2n+1)! has 2a(n)+1 real roots.
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3
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0, 1, 0, 1, 2, 1, 2, 3, 2, 3, 2, 3, 4, 3, 4, 3, 4, 5, 4, 5, 6, 5, 6, 5, 6, 7, 6, 7, 8, 7, 8, 7, 8, 9, 8, 9, 8, 9, 10, 9, 10, 11, 10, 11, 10, 11, 12, 11, 12, 11, 12, 13, 12, 13, 14, 13, 14, 13, 14, 15, 14, 15, 16
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OFFSET
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0,5
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COMMENTS
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Let phi be the golden mean. Let B be the generalized Beatty sequence B(n):= 2*floor(n*phi) - 3*n, n = 0,1,2,... Then a(n) = B(n+5) for n = 0,...,200, except for n = 84, 118, 152, 165, 173, 186. - Michel Dekking, Mar 30 2020
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REFERENCES
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James Propp, posting to math-fun mailing list May 30 1997.
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LINKS
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MATHEMATICA
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f[n_] := Sum[(-1)^k*x^(2*k + 1)/(2*k + 1)!, {k, 0, n}]; a[n_] := (CountRoots[f[n], x] - 1)/2; Table[a[n], {n, 0, 62}] (* Jean-François Alcover, Apr 16 2013 *)
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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