0,2

a(n)^2 - 42 (2*b(n))^2 = +1 with b(n):=A097309(n) gives all nonnegative 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)=26*a(n-1) - a(n-2), a(-1) := 13, a(0)=1.

a(n)= T(n, 13)= (S(n, 26)-S(n-2, 26))/2 = S(n, 26)-13*S(n-1, 26) with T(n, x), resp. S(n, x), Chebyshev's polynomials of the first, resp.second, kind. See A053120 and A049310. S(n, 26)=A097309(n).

a(n)= (ap^n + am^n)/2 with ap := 13+2*sqrt(42) and am := 13-2*sqrt(42).

a(n)= sum(((-1)^k)*(n/(2*(n-k)))*binomial(n-k, k)*(2*13)^(n-2*k), k=0..floor(n/2)), n>=1.

G.f.: (1-13*x)/(1-26*x+x^2).

a(n) = Cosh[2n*ArcSinh[Sqrt[6]]] - Herbert Kociemba (kociemba(AT)t-online.de), Apr 24 2008

Cf. a(n)=sqrt(1 + 168*A097309(n)^2), n>=0.

Sequence in context: A012492 A142543 A029807 this_sequence A041315 A041312 A096717

Adjacent sequences: A097305 A097306 A097307 this_sequence A097309 A097310 A097311

nonn,easy

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