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

Author

Greg Dresden and Tracy Z. Wu, Sep 03 2020

Keywords

• nonn
• easy

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A000032, A049685, first differences of A049668.

Programs

Mathematica

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

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