login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A020542 a(n) = 5th Chebyshev polynomial (second kind) evaluated at 2^n. 1
6, 780, 30744, 1032240, 33423456, 1072693440, 34351350144, 1099444519680, 35183835219456, 1125895611878400, 36028762659231744, 1152921229728952320, 36893485948395872256, 1180591603125225308160, 37778931722219673452544, 1208925818488729268060160 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Colin Barker, Table of n, a(n) for n = 0..663

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (42,-336,512).

FORMULA

From Colin Barker, May 03 2015: (Start)

  a(n) = 2^(1+n)*(3-4^(2+n)+16^(1+n))

  a(n) = 42*a(n-1)-336*a(n-2)+512*a(n-3) for n>2.

  G.f.: -6*(88*x+1) / ((2*x-1)*(8*x-1)*(32*x-1)).

(End)

MAPLE

with(orthopoly):seq(U(5, 2^i), i=0..24);

MATHEMATICA

Table[ChebyshevU[5, 2^n], {n, 1, 40}] (* Vladimir Joseph Stephan Orlovsky, Nov 03 2009 *)

LinearRecurrence[{42, -336, 512}, {6, 780, 30744}, 16] (* Jean-Fran├žois Alcover, Dec 04 2017 *)

PROG

(PARI) Vec(-6*(88*x+1)/((2*x-1)*(8*x-1)*(32*x-1)) + O(x^100)) \\ Colin Barker, May 03 2015

(PARI) a(n) = polchebyshev(5, 2, 2^n) \\ Michel Marcus, May 03 2015

CROSSREFS

Sequence in context: A214009 A088217 A242850 * A045480 A006114 A321426

Adjacent sequences:  A020539 A020540 A020541 * A020543 A020544 A020545

KEYWORD

nonn,easy

AUTHOR

Simon Plouffe

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 6 14:15 EST 2019. Contains 329806 sequences. (Running on oeis4.)