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A012265 x - x^3/3! + x^5/5! - ... + (-1)^n*x^(2n+1)/(2n+1)! has 2a(n)+1 real roots. 2
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Apr 16 2013 *)

CROSSREFS

Cf. A012264.

Sequence in context: A283431 A258594 A086520 * A268835 A006641 A191408

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

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Last modified July 10 11:42 EDT 2020. Contains 335576 sequences. (Running on oeis4.)