0,2

Chebyshev's polynomials U(n,x) evaluated at x=6.

a(n) give all (nontrivial, integer) solutions of Pell equation b(n)^2 - 35*a(n)^2 = +1 with b(n)=A023038(n+1), n>=0.

Index entries for sequences related to linear recurrences with constant coefficients

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

a(n) = S(n, 12) with S(n, x) := U(n, x/2) Chebyshev's polynomials of the second kind. See A049310.

a(n) = ((6+sqrt(35))^(n+1) - (6-sqrt(35))^(n+1))/(2*sqrt(35)).

a(n) = sqrt((A023038(n)^2 - 1)/35).

[A077417(n), a(n)] = the 2 X 2 matrix [1,10; 1,11]^(n+1) * [1,0]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 19 2008

a(n)=12*a(n-1)-a(n-2)for n>1, a(0)=1, a(1)=12. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 17 2008]

lst={}; Do[AppendTo[lst, GegenbauerC[n, 1, 6]], {n, 0, 8^2}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 11 2008]

sage: [lucas_number1(n, 12, 1) for n in xrange(1, 20)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 25 2008

Cf. A077417.

Adjacent sequences: A004188 A004189 A004190 this_sequence A004192 A004193 A004194

Sequence in context: A056340 A056330 A163448 this_sequence A051051 A001021 A000468

nonn

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

Chebyshev comments and a(n) formulas from W. Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Nov 08 2002