A020540 a(n) = 8^(n+1) - 2^(n+2).

4, 56, 496, 4064, 32704, 262016, 2096896, 16776704, 134216704, 1073739776, 8589930496, 68719468544, 549755797504, 4398046478336, 35184372023296, 281474976579584, 2251799813423104, 18014398508957696, 144115188074807296

Offset

0,1

Comments

Third Chebyshev polynomial of second kind evaluated at 2^n.

Links

Table of n, a(n) for n=0..18.

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (10, -16).

Formula

G.f.: 4(1+4x)/(1-10x+16x^2).

a(0)=4, a(1)=56, a(n) = 10*a(n-1) - 16*a(n-2). - Harvey P. Dale, Feb 27 2013

Example

U_3(x) = 8x^3 - 4x so U_3(2^n) = 8(2^n)^3 - 4(2^n) = 8^(n+1) - 2^(n+2).

Maple

with(orthopoly):seq(U(3, 2^i), i=0..24);

Mathematica

Table[ChebyshevU[3, 2^n], {n, 1, 40}] (* Vladimir Joseph Stephan Orlovsky, Nov 03 2009 *)
Table[8^(n+1)-2^(n+2), {n, 0, 20}] (* or *) LinearRecurrence[{10, -16}, {4, 56}, 20] (* Harvey P. Dale, Feb 27 2013 *)

Prog

(PARI) a(n)=if(n<0, 0, 8^(n+1)-2^(n+2))

Crossrefs

Sequence in context: A201620 A204108 A077122 * A101540 A358882 A224181

Adjacent sequences: A020537 A020538 A020539 * A020541 A020542 A020543

Keyword

nonn

Author

Simon Plouffe

Status

approved