A350904 Denominators 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).

1, 1, 1, 1, 3, 5, 4, 195, 28, 4420, 1001, 550732, 94248, 20757737, 150585864, 596098336680, 84878386593, 17090110926980520, 1216260982575912, 13296541287045886485, 484071647034823848, 3418959485072391296664264, 19630886922468003512297

Offset: 0

Author

Amiram Eldar, Jan 21 2022

Keywords

• nonn
• frac
• easy

Comments

See A350902 for details.

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, A350903 (numerators).

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]); Denominator @ Array[u, 25, 0]]