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A020541 a(n) = 4th Chebyshev polynomial (second kind) evaluated at 2^n. 1
5, 209, 3905, 64769, 1045505, 16764929, 268386305, 4294770689, 68718690305, 1099508482049, 17592173461505, 281474926379009, 4503599426043905, 72057593232621569, 1152921501385621505, 18446744060824649729, 295147905127813218305, 4722366482663486783489 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Colin Barker, Table of n, a(n) for n = 0..829

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (21,-84,64).

FORMULA

a(n) = 16^(n+1) - 3*4^(n+1) + 1.

a(n) = 21*a(n-1) - 84*a(n-2) + 64*a(n-3) for n>2. - Colin Barker, May 03 2015

G.f.: (64*x^2-104*x-5) / ((x-1)*(4*x-1)*(16*x-1)). - Colin Barker, May 03 2015

MAPLE

with(orthopoly):seq(U(4, 2^i), i=0..24);

MATHEMATICA

Table[ChebyshevU[4, 2^n], {n, 1, 40}] (* Vladimir Joseph Stephan Orlovsky, Nov 03 2009 *)

PROG

(PARI) Vec((64*x^2-104*x-5)/((x-1)*(4*x-1)*(16*x-1)) + O(x^100)) \\ Colin Barker, May 03 2015

(PARI) a(n) = polchebyshev(4, 2, 2^n) \\ Michel Marcus, May 03 2015

CROSSREFS

Sequence in context: A292330 A068531 A144139 * A027682 A006413 A055316

Adjacent sequences:  A020538 A020539 A020540 * A020542 A020543 A020544

KEYWORD

nonn,easy

AUTHOR

Simon Plouffe

STATUS

approved

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Last modified November 18 19:48 EST 2019. Contains 329288 sequences. (Running on oeis4.)