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Revision History for A332420

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A332420

Number of Maclaurin polynomials of sin x having exactly n positive zeros.
(history; published version)

#6 by N. J. A. Sloane at Mon Mar 09 15:11:56 EDT 2020

STATUS

proposed

approved

#5 by Clark Kimberling at Sat Mar 07 17:30:56 EST 2020

STATUS

editing

proposed

#4 by Clark Kimberling at Sat Mar 07 17:28:44 EST 2020

KEYWORD

nonn,easy,hard,more

STATUS

proposed

editing

#3 by Clark Kimberling at Thu Feb 13 09:55:19 EST 2020

STATUS

editing

proposed

Discussion

Fri Mar 06

23:11

N. J. A. Sloane: Both "easy" and "more" again?

#2 by Clark Kimberling at Thu Feb 13 09:52:01 EST 2020

NAME

allocated for Clark KimberlingNumber of Maclaurin polynomials of sin x having exactly n positive zeros.

DATA

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.

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.

KEYWORD

allocated

nonn,easy,more

AUTHOR

Clark Kimberling, Feb 13 2020

STATUS

approved

editing

#1 by Clark Kimberling at Wed Feb 12 13:31:20 EST 2020

NAME

allocated for Clark Kimberling

KEYWORD

allocated

STATUS

approved