A097771 Chebyshev U(n,x) polynomial evaluated at x=339=2*13^2+1.

1, 678, 459683, 311664396, 211308000805, 143266512881394, 97134484425584327, 65857037174033292312, 44650974069510146603209, 30273294562090705363683390, 20525249062123428726430735211

Offset

0,2

Comments

Used to form integer solutions of Pell equation a^2 - 170*b^2 =-1. See A097772 with A097773.

Links

Table of n, a(n) for n=0..10.

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (678, -1).

Formula

a(n) = 2*339*a(n-1) - a(n-2), n>=1, a(0)=1, a(-1):=0.

a(n) = S(n, 2*339)= U(n, 339), Chebyshev's polynomials of the second kind. See A049310.

G.f.: 1/(1-2*339*x+x^2).

a(n)= sum((-1)^k*binomial(n-k, k)*678^(n-2*k), k=0..floor(n/2)), n>=0.

a(n) = ((339+26*sqrt(170))^(n+1) - (339-26*sqrt(170))^(n+1))/(52*sqrt(170)), n>=0.

Mathematica

LinearRecurrence[{678, -1}, {1, 678}, 11] (* Ray Chandler, Aug 12 2015 *)

Crossrefs

Sequence in context: A251830 A250872 A186127 * A121105 A046514 A199995

Adjacent sequences: A097768 A097769 A097770 * A097772 A097773 A097774

Keyword

nonn,easy

Author

Wolfdieter Lang, Aug 31 2004

Status

approved