A332420 Number of Maclaurin polynomials of sin x having exactly n positive zeros.

3, 4, 5, 4, 4, 4, 4, 5, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 5, 4, 4, 4, 4, 5

Offset

1,1

Comments

a(1) counts these values of 2n-1: 3, 5, and 11. The single zeros of p(3,x), p(5,x), and p(11,x) are sqrt(6), 3.078642..., and 3.141148..., respectively.

Links

Table of n, a(n) for n=1..32.

Mathematica

z = 60; p[n_, x_] := Normal[Series[Sin[x], {x, 0, n}]];
t[n_] := x /. NSolve[p[n, x] == 0, x, z];
u[n_] := Select[t[n], Im[#] == 0 && # > 0 &];
v = Table[Length[u[n]], {n, 2, 30}]
(1/2) Table[Count[v, n], {n, 1, 40}]

Crossrefs

Cf. A332417, A332325.

Sequence in context: A275719 A014250 A155078 * A115051 A094634 A114545

Adjacent sequences: A332417 A332418 A332419 * A332421 A332422 A332423

Keyword

nonn,hard,more

Author

Clark Kimberling, Feb 13 2020

Status

approved