The On-Line Encyclopedia of Integer Sequences (OEIS)

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A097842

Chebyshev polynomials S(n,123) + S(n-1,123) with Diophantine property.
(history; published version)

#48 by Charles R Greathouse IV at Thu Sep 08 08:45:14 EDT 2022

PROG

(MAGMAMagma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (1+x)/(1-123*x+x^2) )); // G. C. Greubel, Jan 13 2019

Discussion

Thu Sep 08

08:45

OEIS Server: https://oeis.org/edit/global/2944

#47 by Bruno Berselli at Wed Jan 22 03:31:53 EST 2020

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proposed

approved

#46 by Michel Marcus at Wed Jan 22 02:26:57 EST 2020

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editing

proposed

#45 by Michel Marcus at Wed Jan 22 02:26:46 EST 2020

LINKS

H. C. Williams and R. K. Guy, <a href="http://www.emis.de/journals/INTEGERS/papers/a17self/a17self.Abstract.html ">Some Monoapparitic Fourth Order Linear Divisibility Sequences</a> Integers, Volume 12A (2012) The John Selfridge Memorial Volume.

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proposed

editing

#44 by Jon E. Schoenfield at Tue Jan 21 23:39:51 EST 2020

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editing

proposed

#43 by Jon E. Schoenfield at Tue Jan 21 23:39:48 EST 2020

FORMULA

a(n) = (-2/11)*Ii*((-1)^n)*T(2*n+1, 11*Ii/2) with the imaginary unit I i and Chebyshev's polynomials of the first kind. See the T-triangle A053120.

a(n) = 123*a(n-1) - a(n-2) for n > 1, a(0)=1, a(1)=124 . - Philippe Deléham, Nov 18 2008

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approved

editing

#42 by Susanna Cuyler at Fri Apr 19 13:40:55 EDT 2019

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reviewed

approved

#41 by Michel Marcus at Fri Apr 19 13:30:55 EDT 2019

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proposed

reviewed

#40 by Michael De Vlieger at Fri Apr 19 13:00:48 EDT 2019

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editing

proposed

#39 by Michael De Vlieger at Fri Apr 19 13:00:43 EDT 2019

LINKS

Giovanni Lucca, <a href="http://forumgeom.fau.edu/FG2019volume19/FG201902index.html">Integer Sequences and Circle Chains Inside a Hyperbola</a>, Forum Geometricorum (2019) Vol. 19, 11-16.

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approved

editing