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A282701 a(n) = maximal number of real roots of any of the polynomials c_0 + c_1*x + c_2*x^2 + ... + c_n*x^n where the coefficients c_i are -1, 0, or 1, c_0 != 0, and c_n != 0. 2
0, 1, 2, 3, 2, 3, 4, 5, 4, 5, 4, 5, 6, 7, 6, 7, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The roots are counted with multiplicity (and are nonzero, by definition).

Unlike A282692, this sequence is not monotonic.

A282692(n) >= a(n) >= A282691(n). A282692(n) = max(A282692(n-1),a(n)). Differs from A282691 for n = 6, 12, 13 (and most likely other values of n). - Chai Wah Wu, Feb 25 2017

LINKS

Table of n, a(n) for n=0..16.

EXAMPLE

a(1) = 1 from 1-x.

a(2) = 2 from 1+x-x^2.

a(3) = 3 from 1-x-x^2+x^3 = (1-x)*(1-x^2).

a(5) = 3 from x^5-x^4+x^3-x^2-x+1. - Robert Israel, Feb 26 2017

a(7) = 5 from x^7 + x^6 - x^5 - x^4 - x^3 - x^2 + x + 1 = (x - 1)^2*(x + 1)^3*(x^2 + 1). - Chai Wah Wu and W. Edwin Clark, Feb 23 2017

a(13) = 7 from x^13 + x^12 - x^11 - x^10 - x^9 - x^8 + x^5 + x^4 + x^3 + x^2 - x - 1 = (x - 1)^3*(x + 1)^4*(x^2 + 1)*(x^2 - x + 1)*(x^2 + x + 1). - Chai Wah Wu, Feb 24 2017

CROSSREFS

Cf. A282691, A282692.

Sequence in context: A064289 A078759 A276439 * A095207 A065362 A083219

Adjacent sequences:  A282698 A282699 A282700 * A282702 A282703 A282704

KEYWORD

nonn,more

AUTHOR

Oanh Nguyen and N. J. A. Sloane, Feb 23 2017

EXTENSIONS

a(13) corrected by Chai Wah Wu, Feb 25 2017

a(15)-a(16) added by Luca Petrone, Feb 26 2017

STATUS

approved

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Last modified November 13 19:25 EST 2018. Contains 317149 sequences. (Running on oeis4.)