A088166 Smallest integer divisible by Fibonacci(2n) such that the second partial quotient in the continued fraction expansion of a(n)/phi is 2 (phi is the golden ratio), n >= 2.

12, 72, 504, 3410, 23184, 159094, 1089648, 7465176, 51170460, 350713222, 2403763488, 16475700746, 112925875764, 774004377960, 5305106018016, 36361732975514, 249227005939632, 1708227330997438, 11708364225400920

Offset: 2

Author

Thomas Baruchel, Sep 21 2003

Keywords

• easy
• nonn

Comments

Smallest integer divisible by Fibonacci(2n) such that the continued fraction expansion of a(n)/phi has period 2 or 4.

Crossrefs

Cf. A087954.

Formula

a(n) = Fibonacci(2n)*ceiling(Lucas(2n)/2).

Fibonacci(2n)*(A071618(n)+1). - Thomas Baruchel, Nov 26 2003

Empirical g.f.: -2*x^2*(x^7 - 7*x^6 - 17*x^4 + 131*x^3 - 6*x^2 + 6*x - 6) / ((x^2 - 7*x + 1)*(x^2 - 3*x + 1)*(x^4 + 3*x^3 + 8*x^2 + 3*x + 1)). - Colin Barker, Jan 11 2014