-1,3

b(n)^2 - 42*(2*a(n))^2 = +1 with b(n):=A097308(n) gives all nonnegative integer solutions of this D:=42*4=168 Pell equation.

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, 26) = U(n, 13), n>=-1, with Chebyshev polynomials of 2nd kind. See A049310 for the triangle of S(n, x) coefficients. S(-1, x) := 0 =: U(-1, x).

a(n)= ((13+2*sqrt(42))^n - (13-2*sqrt(42))^n)/(4*sqrt(42)), (Binet form).

a(n)= sum(((-1)^k)*binomial(n-k, k)*26^(n-2*k), k=0..floor(n/2)).

G.f.: 1/(1-26*x+x^2).

a(n)=26*a(n-1)-a(n-2), a(-1)=0, a(0)=1. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 18 2008]

lst={}; Do[AppendTo[lst, GegenbauerC[n, 1, 13]], {n, 0, 8^2}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 11 2008]

sage: [lucas_number1(n, 26, 1) for n in xrange(0, 20)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 25 2008

a(n) = sqrt((A097308(n)^2 - 1)/168).

Sequence in context: A014913 A106793 A158542 this_sequence A009970 A041313 A042302

Adjacent sequences: A097306 A097307 A097308 this_sequence A097310 A097311 A097312

nonn,easy

Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Aug 31 2004