A012265 x - x^3/3! + x^5/5! - ... + (-1)^n*x^(2n+1)/(2n+1)! has 2a(n)+1 real roots.

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

Offset

0,5

Comments

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

References

James Propp, posting to math-fun mailing list May 30 1997.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Mathematica

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 *)

Crossrefs

Cf. A012264.

Sequence in context: A258594 A364215 A086520 * A339765 A268835 A006641

Adjacent sequences: A012262 A012263 A012264 * A012266 A012267 A012268

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Extensions

More terms from James A. Sellers

Status

approved