A350903 Numerators of the sequence of fractions defined by u(n) = ((5*F(n)*F(n-1)*F(2*n-1)*u(n-1) + F(n-1)*L(n)*u(n-2))/(L(n-1)*F(n))), with u(0) = 0 and u(1) = 1, where F(n) = A000045(n) and L(n) = A000032(n).

0, 1, 10, 84, 8225, 999146, 161691205, 4081394133187, 801267937794945, 451272063930179690869, 955797228958312695758495, 12869303093903467063139191673469, 141131682569461636438244407470674215, 5214528077594695050414454970728001934806021

Offset: 0

Author

Amiram Eldar, Jan 21 2022

Keywords

• nonn
• frac
• easy

Comments

See A350902 for details.

Examples

			The sequence of fractions begins with 0, 1, 10, 84, 8225/3, 999146/5, 161691205/4, 4081394133187/195, 801267937794945/28, 451272063930179690869/4420, ...
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..60
• Richard André-Jeannin, Sequences of Integers Satisfying Recurrence Relations, The Fibonacci Quarterly, Vol. 29, No. 3 (1991), pp. 205-208.

Crossrefs

Cf. A000032, A000045, A079586, A350902, A350904 (denominators).

Programs

Mathematica

With[{F = Fibonacci, L = LucasL}, u[0] = 0; u[1] = 1; u[n_] := u[n] = (5*F[n]*F[n - 1]*F[2*n - 1]*u[n - 1] + F[n - 1]*L[n]*u[n - 2])/(L[n - 1]*F[n]); Numerator @ Array[u, 15, 0]]