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

Author

Simon Plouffe

Keywords

• nonn

Comments

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

Examples

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

Links

• Index entries for sequences related to Chebyshev polynomials.
• Index entries for linear recurrences with constant coefficients, signature (10, -16).

Programs

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 *)

PARI

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

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