The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A144138 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A144138

Chebyshev polynomial of the second kind U(3,n).
(history; published version)

#13 by Harvey P. Dale at Fri Dec 23 18:55:05 EST 2022

STATUS

editing

approved

#12 by Harvey P. Dale at Fri Dec 23 18:55:03 EST 2022

LINKS

<a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

MATHEMATICA

LinearRecurrence[{4, -6, 4, -1}, {0, 4, 56, 204}, 40] (* Harvey P. Dale, Dec 23 2022 *)

STATUS

approved

editing

#11 by Charles R Greathouse IV at Thu Sep 08 08:45:38 EDT 2022

PROG

(MAGMAMagma) [8*n^3-4*n: n in [0..40]]; // Vincenzo Librandi, May 29 2014

Discussion

Thu Sep 08

08:45

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

#10 by Bruno Berselli at Thu May 29 10:16:22 EDT 2014

STATUS

editing

approved

#9 by Bruno Berselli at Thu May 29 10:16:19 EDT 2014

NAME

Chebyshev polynomial of the second kind U_(3(,n).

#8 by Bruno Berselli at Thu May 29 10:15:43 EDT 2014

NAME

ChebyshevU[3,n].

Chebyshev polynomial of the second kind U_3(n).

STATUS

proposed

editing

#7 by Vincenzo Librandi at Thu May 29 04:41:38 EDT 2014

STATUS

editing

proposed

#6 by Vincenzo Librandi at Thu May 29 04:41:00 EDT 2014

LINKS

Vincenzo Librandi, <a href="/A144138/b144138.txt">Table of n, a(n) for n = 0..1000</a>

FORMULA

G.f.: 4*x*(1 + 10*x + x^2)/(1 - x)^4. - Vincenzo Librandi, May 29 2014

a(n) = 4*n*(2*n^2-1). - Vincenzo Librandi, May 29 2014

MATHEMATICA

CoefficientList[Series[4 x (1 + 10 x + x^2)/(1 - x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, May 29 2014 *)

PROG

(MAGMA) [8*n^3-4*n: n in [0..40]]; // Vincenzo Librandi, May 29 2014

KEYWORD

nonn,easy

STATUS

approved

editing

#5 by Russ Cox at Sat Mar 31 12:38:16 EDT 2012

AUTHOR

_Vladimir Joseph Stephan Orlovsky (4vladimir(AT)gmail.com), _, Sep 11 2008

Discussion

Sat Mar 31

12:38

OEIS Server: https://oeis.org/edit/global/876

#4 by T. D. Noe at Thu Jun 30 21:53:10 EDT 2011

STATUS

proposed

approved