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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 G. C. Greubel, Table of n, a(n) for n = 0..10 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 Cf. A000045, A058635, A058891, A081460, A083696. Sequence in context: A262206 A240993 A007079 * A110131 A112332 A101339 Adjacent sequences: A083694 A083695 A083696 * A083698 A083699 A083700 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.)