

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, 7, 8, 7, 8, 7
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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(n1),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..21.


EXAMPLE

a(1) = 1 from 1x.
a(2) = 2 from 1+xx^2.
a(3) = 3 from 1xx^2+x^3 = (1x)*(1x^2).
a(5) = 3 from x^5x^4+x^3x^2x+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
a(17)a(21) from Max Alekseyev, Jan 28 2022


STATUS

approved



