A000304 a(n) = a(n-1)*a(n-2).

2, 3, 6, 18, 108, 1944, 209952, 408146688, 85691213438976, 34974584955819144511488, 2997014624388697307377363936018956288, 104819342594514896999066634490728502944926883876041385836544

Offset: 2

Author

N. J. A. Sloane

Keywords

• nonn

Comments

A038500(a(n)) = A010098(n-2); for n > 2: A006519(a(n)) = A000301(n-3); A001222(a(n)) = A000045(n-1). - Reinhard Zumkeller, Jul 06 2014

Links

• T. D. Noe, Table of n, a(n) for n = 2..18
• Peter G. Anderson, Notes & Extensions for a Remarkable Continued Fraction, Fibonacci Quart. 55 (2017), no. 5, 9-14. Mentions this sequence.
• Sergio Falcon, Fibonacci's multiplicative sequence, Int. J. Math. Edu. Sci. Technol. 34-2 (2003), 310-315. [_Sergio Falcon_, Nov 23 2009]

Crossrefs

Cf. A000045, A000301, A001222, A006519, A010098, A038500, A249406.

Programs

Haskell

a000304 n = a000304_list !! (n-2)
a000304_list = 2 : 3 : zipWith (*) a000304_list (tail a000304_list)
-- Reinhard Zumkeller, Jul 06 2014

Maple

A000304 := proc(n) option remember; if n <=3 then n else A000304(n-1)*A000304(n-2); fi; end;

Mathematica

nxt[{a_,b_}]:={b,a*b}; Transpose[NestList[nxt,{2,3},12]][[1]] (* Harvey P. Dale, Nov 16 2014 *)

Formula

For n>=4, a(n) = 2^A000045(n-3)*3^A000045(n-2). - Benoit Cloitre, Sep 26 2003

For n > 2: a(n) = A000301(n-3) * A010098(n-2). - Reinhard Zumkeller, Jul 06 2014

Extensions

More terms from Vladimir Joseph Stephan Orlovsky, Feb 17 2010