

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 mathfun 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}] (* JeanFrançois 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



