The On-Line Encyclopedia of Integer Sequences (OEIS)

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A077412

Chebyshev U(n,x) polynomial evaluated at x=8.
(history; published version)

#57 by G. C. Greubel at Sun Dec 22 23:53:00 EST 2019

MATHEMATICA

Table[GegenbauerC[n, 1, 8]], , {n, 0, 20}] (* Vladimir Joseph Stephan Orlovsky, Sep 11 2008 *)

STATUS

proposed

editing

#56 by G. C. Greubel at Sun Dec 22 23:52:18 EST 2019

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editing

proposed

#55 by G. C. Greubel at Sun Dec 22 23:52:14 EST 2019

MAPLE

seq( simplify(ChebyshevU(n, 8)), n=0..20); # G. C. Greubel, Dec 22 2019

MATHEMATICA

lst={}; Do[AppendToTable[lst, GegenbauerC[n, 1, 8]], {n, 0, 8^220}]; lst (* Vladimir Joseph Stephan Orlovsky, Sep 11 2008 *)

CoefficientList[Series[1/(1 - 16 x 16x+ x^2), {x, 0, 4020}], x] (* Vincenzo Librandi, Dec 24 2012 *)

ChebyshevU[Range[21] -1, 8] (* G. C. Greubel, Dec 22 2019 *)

PROG

(Sage) [chebyshev_U(n, 8) for n in (0..20)] # G. C. Greubel, Dec 22 2019

(PARI) x='x+O('x^30); Vecvector(1/ 21, n, polchebyshev(n-1 - 16*x + x^, 2, 8) ) \\ G. C. Greubel, Jan 18 2018

(GAP) m:=8;; a:=[1, 2*m];; for n in [3..20] do a[n]:=2*m*a[n-1]-a[n-2]; od; a; # G. C. Greubel, Dec 22 2019

CROSSREFS

Chebyshev sequence U(n, m): A000027 (m=1), A001353 (m=2), A001109 (m=3), A001090 (m=4), A004189 (m=5), A004191 (m=6), A007655 (m=7), this sequence (m=8), A049660 (m=9), A075843 (m=10), A077421 (m=11), A077423 (m=12), A097309 (m=13), A097311 (m=14), A097313 (m=15), A029548 (m=16), A029547 (m=17), A144128 (m=18), A078987 (m=19), A097316 (m=33).

Cf. A323182.

STATUS

approved

editing

#54 by N. J. A. Sloane at Sat Dec 07 12:18:24 EST 2019

PROG

(Sage) [lucas_number1(n, 16, 1) for n in xrangerange(1, 20)] # Zerinvary Lajos, Jun 25 2008

Discussion

Sat Dec 07

12:18

OEIS Server: https://oeis.org/edit/global/2837

#53 by Sean A. Irvine at Thu Jun 06 19:00:39 EDT 2019

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reviewed

approved

#52 by Felix Fröhlich at Thu Jun 06 16:43:20 EDT 2019

STATUS

proposed

reviewed

#51 by Michael De Vlieger at Thu Jun 06 16:35:59 EDT 2019

STATUS

editing

proposed

#50 by Michael De Vlieger at Thu Jun 06 16:35:56 EDT 2019

LINKS

Pablo Lam-Estrada, Myriam Rosalía Maldonado-Ramírez, José Luis López-Bonilla, Fausto Jarquín-Zárate, <a href="https://arxiv.org/abs/1904.13002">The sequences of Fibonacci and Lucas for each real quadratic fields Q(Sqrt(d))</a>, arXiv:1904.13002 [math.NT], 2019.

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approved

editing

#49 by N. J. A. Sloane at Fri Jan 19 02:12:23 EST 2018

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reviewed

approved

#48 by Michel Marcus at Fri Jan 19 01:06:34 EST 2018

STATUS

proposed

reviewed