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A282701
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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.
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2
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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
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0,3
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COMMENTS
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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
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LINKS
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Table of n, a(n) for n=0..21.
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EXAMPLE
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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
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CROSSREFS
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Cf. A282691, A282692.
Sequence in context: A064289 A078759 A276439 * A095207 A065362 A083219
Adjacent sequences: A282698 A282699 A282700 * A282702 A282703 A282704
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KEYWORD
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nonn,more
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AUTHOR
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Oanh Nguyen and N. J. A. Sloane, Feb 23 2017
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EXTENSIONS
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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
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STATUS
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approved
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