A333718 a(n) = L(8*n+4)/7, where L=A000032 (the Lucas sequence).

1, 46, 2161, 101521, 4769326, 224056801, 10525900321, 494493258286, 23230657239121, 1091346396980401, 51270050000839726, 2408601003642486721, 113152977121196036161, 5315781323692571212846, 249728569236429650967601, 11731926972788501024264401, 551150839151823118489459246

Offset

0,2

Comments

a(n) is the denominator of the continued fraction [3*sqrt(5), 3*sqrt(5),..., 3*sqrt(5)] with 2n+1 terms.

a(n) = (2/7)*T(2*n+1, 7/2), where T(n,x) denotes the n-th Chebyshev polynomial of the first kind. - Peter Bala, Jul 08 2022

Links

Table of n, a(n) for n=0..16.

Index entries for linear recurrences with constant coefficients, signature (47,-1).

Formula

a(n) = 47*a(n-1) - a(n-2) for n>2.

G.f.: (1-x)/(1-47*x+x^2). - R. J. Mathar, Sep 03 2020

Example

The continued fraction [3*sqrt(5), 3*sqrt(5), 3*sqrt(5)] with 2*1 + 1 terms equals 141*sqrt(5)/46, and 46 is our a(1) term.

Mathematica

Table[LucasL[8 n + 4]/7, {n, 0, 20}]

Crossrefs

Cf. A000032, A049685, first differences of A049668.

Sequence in context: A223971 A009990 A042013 * A234153 A123830 A201234

Adjacent sequences: A333715 A333716 A333717 * A333719 A333720 A333721

Keyword

nonn,easy

Author

Greg Dresden and Tracy Z. Wu, Sep 03 2020

Status

approved