OFFSET
1,3
LINKS
Harry J. Smith, Table of n, a(n) for n = 1..18
FORMULA
Limit_{n->oo} log(a(n))/log(a(n-1)) = phi. - Gerald McGarvey, Jul 25 2004
Limit_{n->oo} log(a(n))/log(a(n-1)) = phi follows from Stirling's approximation and the approximation log(F(n)) = n log(phi) + O(1). In fact, log(a(n)) = K phi^n + O(n); the value of K does not matter for this result, but it is log(phi)/phi. - Franklin T. Adams-Watters, Dec 14 2006
a(n) ~ 5^(1/4) * phi^(3/2 - n/2 + phi^(n-1)) / sqrt(2*Pi), where phi = (1+sqrt(5))/2 = A001622. - Vaclav Kotesovec, Nov 13 2014
EXAMPLE
a(7) = binomial(Fibonacci(8), Fibonacci(7)) = binomial(21, 13) = 1287.
MATHEMATICA
Table[ Binomial[ Fibonacci[n], Fibonacci[n - 1]], {n, 1, 14} ]
Binomial[Last[#], First[#]]&/@Partition[Fibonacci[Range[0, 15]], 2, 1] (* Harvey P. Dale, Oct 15 2014 *)
PROG
(PARI) { for (n=1, 18, a=binomial(fibonacci(n), fibonacci(n-1)); write("b066526.txt", n, " ", a) ) } \\ Harry J. Smith, Feb 21 2010
CROSSREFS
KEYWORD
easy,nice,nonn
AUTHOR
Joe Faust, Jan 05 2002
EXTENSIONS
Edited by Robert G. Wilson v, Jan 07 2002
Minor edits by Vaclav Kotesovec, Nov 13 2014
STATUS
approved