cp's OEIS Frontend

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).

%I A350904 #12 Jan 05 2025 19:51:42
%S A350904 1,1,1,1,3,5,4,195,28,4420,1001,550732,94248,20757737,150585864,
%T A350904 596098336680,84878386593,17090110926980520,1216260982575912,
%U A350904 13296541287045886485,484071647034823848,3418959485072391296664264,19630886922468003512297
%N 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).
%C A350904 See A350902 for details.
%H A350904 Amiram Eldar, <a href="/A350904/b350904.txt">Table of n, a(n) for n = 0..60</a>
%H A350904 Richard André-Jeannin, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/29-3/andre-jeannin2.pdf">Sequences of Integers Satisfying Recurrence Relations</a>, The Fibonacci Quarterly, Vol. 29, No. 3 (1991), pp. 205-208.
%t A350904 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]]
%Y A350904 Cf. A000032, A000045, A079586, A350902, A350903 (numerators).
%K A350904 nonn,frac,easy
%O A350904 0,5
%A A350904 _Amiram Eldar_, Jan 21 2022