OFFSET
1,1
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..798
Hideyuki Ohtskua, proposer, Problem H-944, Advanced Problems and Solutions, The Fibonacci Quarterly, Vol. 62, No. 3 (2024), p. 266.
Index entries for linear recurrences with constant coefficients, signature (13,104,-260,-260,104,13,-1).
FORMULA
Sum_{n>=1} (-1)^(n+1)/a(n) = (sqrt(5) - 2)/ 4 = A204188 - 1/2 (Ohtskua, 2024).
G.f.: -x^2*(-20+65*x+195*x^2-84*x^3-13*x^4+x^5)/ ( (1+x) *(x^2-3*x+1) *(x^2+7*x+1) *(x^2-18*x+1) ). - R. J. Mathar, Aug 30 2024
MATHEMATICA
a[n_] := LucasL[n-1] * LucasL[n+1] * Fibonacci[2*n-1] * Fibonacci[2*n+1]; Array[a, 20]
PROG
(PARI) lucas(n) = fibonacci(n-1) + fibonacci(n+1);
a(n) = lucas(n-1) * lucas(n+1) * fibonacci(2*n-1) * fibonacci(2*n+1);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Aug 29 2024
STATUS
approved