A020538 a(n) = 4th Chebyshev polynomial (first kind) evaluated at 2^n.

1, 97, 1921, 32257, 522241, 8380417, 134184961, 2147352577, 34359214081, 549753716737, 8796084633601, 140737454800897, 2251799679467521, 36028796482093057, 576460750155939841, 9223372028264841217, 147573952555316674561, 2361183241297383653377

Offset

0,2

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

From Colin Barker, May 03 2015: (Start)

a(n) = (1-2^(3+2*n)+2^(3+4*n)).

a(n) = 21*a(n-1)-84*a(n-2)+64*a(n-3) for n>2.

G.f.: (32*x^2-76*x-1) / ((x-1)*(4*x-1)*(16*x-1)).

(End)

Maple

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

Mathematica

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

Prog

(PARI) Vec((32*x^2-76*x-1)/((x-1)*(4*x-1)*(16*x-1)) + O(x^100)) \\ Colin Barker, May 03 2015
(PARI) a(n) = polchebyshev(4, 1, 2^n) \\ Michel Marcus, May 03 2015

Crossrefs

Sequence in context: A233433 A162542 A241968 * A359639 A075665 A012839

Adjacent sequences: A020535 A020536 A020537 * A020539 A020540 A020541

Keyword

nonn,easy

Author

Simon Plouffe

Status

approved