cp's OEIS Frontend

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).

%I A350903 #12 Jan 05 2025 19:51:42
%S A350903 0,1,10,84,8225,999146,161691205,4081394133187,801267937794945,
%T A350903 451272063930179690869,955797228958312695758495,
%U A350903 12869303093903467063139191673469,141131682569461636438244407470674215,5214528077594695050414454970728001934806021
%N 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).
%C A350903 See A350902 for details.
%H A350903 Amiram Eldar, <a href="/A350903/b350903.txt">Table of n, a(n) for n = 0..60</a>
%H A350903 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.
%e A350903 The sequence of fractions begins with 0, 1, 10, 84, 8225/3, 999146/5, 161691205/4, 4081394133187/195, 801267937794945/28, 451272063930179690869/4420, ...
%t A350903 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]]
%Y A350903 Cf. A000032, A000045, A079586, A350902, A350904 (denominators).
%K A350903 nonn,frac,easy
%O A350903 0,3
%A A350903 _Amiram Eldar_, Jan 21 2022