OFFSET
0,1
COMMENTS
Third Chebyshev polynomial of second kind evaluated at 2^n.
LINKS
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
KEYWORD
nonn
AUTHOR
STATUS
approved