0,2

Chebyshev sequence U(n,17)=S(n,34) with Diophantine property.

b(n)^2 - 2*(12*a(n))^2 = 1 with the companion sequence b(n)=A056771(n+1).

b(n)^2 - 2*(12*a(n))^2 = 1 where the companion sequence b(n)=A056771(n+1). - Antonio A. Olivares (olivares14031(AT)yahoo.com), Mar 19 2008

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

a(n) = 34*a(n-1) - a(n-2), a(-1) = 0, a(0) = 1.

a(n) = S(n, 34) with S(n, x) := U(n, x/2) Chebyshev's polynomials of the 2nd kind. See A049310.

a(n) = (ap^(n+1) - am^(n+1))/(ap - am) with ap = 17+12*sqrt(2) and am = 17-12*sqrt(2).

a(n) = sum((-1)^k*binomial(n-k, k)*34^(n-2*k), k = 0..floor(n/2)).

a(n) = sqrt((A056771(n+1)^2 -1)/2)/12.

a(n) = 35*a(n-1) - 35*a(n-2) + a(n-3); a(0) = 0, a(1) = 1, a(2) = 34. Also a(n) = (sqrt(2)/48)*((17+12*sqrt(2))^n-(17-12*sqrt(2))^n); a(n) = (sqrt(2)/48)*((3+2*sqrt(2))^2n-(3-2*sqrt(2))^2n); a(n) = (sqrt(2)/48)*((1+sqrt(2))^4n-(1-sqrt(2))^4n). - Antonio A. Olivares (olivares14031(AT)yahoo.com), Mar 19 2008

with (combinat):seq(fibonacci(4*n, 2)/12, n=1..15); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 21 2008

lst={}; Do[AppendTo[lst, GegenbauerC[n, 1, 17]], {n, 0, 8^2}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 11 2008]

(PARI) A029547(n, x=[0, 1], A=[17, 72*4; 1, 17]) = vector(n, i, (x*=A)[1]) - M. F. Hasler, May 26 2007

(Other) sage: [lucas_number1(n, 34, 1) for n in xrange(1, 16)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 07 2009]

A091761 is an essentially identical sequence.

Sequence in context: A098607 A075292 A158696 this_sequence A091761 A009978 A041545

Adjacent sequences: A029544 A029545 A029546 this_sequence A029548 A029549 A029550

nonn

N. J. A. Sloane (njas(AT)research.att.com).

Chebyshev comments from W. Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Dec 11 2002