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A083697 a(n) = 2^(2^n - 1) * Fibonacci(2^n). 2
1, 2, 24, 2688, 32342016, 4677882957791232, 97861912906883207538212742365184, 42829440312913272520181533609472356498655100482256687829780267008 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
A083696(n)/a(n) converges to sqrt(5).
Similar to A081460: a(n) is the denominator of the same mapping f(r)=(1/2)(r+5/r) but with initial value r=1.
LINKS
FORMULA
a(n) = 2*a(n-1)*A083696(n-1).
a(n) = A058635(n) * A058891(n).
a(n) = 2^(2^n - 1) * A000045(2^n).
a(n) = Sum_{r=0..(2^n -1)} (5^r/(2*r+1)!)*Product_{k=0..2*r} (2^n - k).
MATHEMATICA
Table[Sum[Product[2^n -k, {k, 0, 2*r}]k^r/(2*r+1)!, {r, 0, 2^n -1}], {n, 0, 8}]
Table[2^(2^n -1)*Fibonacci[2^n], {n, 0, 8}] (* G. C. Greubel, Jan 14 2022 *)
PROG
(Sage) [2^(2^n -1)*lucas_number1(2^n, 1, -1) for n in (0..8)] # G. C. Greubel, Jan 14 2022
(Magma) [2^(2^n -1)*Fibonacci(2^n): n in [0..8]]; // G. C. Greubel, Jan 14 2022
CROSSREFS
Sequence in context: A262206 A240993 A007079 * A110131 A112332 A101339
KEYWORD
easy,nonn
AUTHOR
Mario Catalani (mario.catalani(AT)unito.it), May 22 2003
EXTENSIONS
The next term is too large to include.
Better description from Ralf Stephan, Aug 29 2004
STATUS
approved

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Last modified February 24 04:32 EST 2024. Contains 370288 sequences. (Running on oeis4.)