A074046 a(n)=a(n-1)*a(n-2)*a(n-3)*(1/a(n-1)+1/a(n-2)+1/a(n-3)) starting with a(1)=a(2)=1 and a(3)=2.

1, 1, 2, 5, 17, 129, 2923, 428951, 1309535519, 565555596556379, 740857737860237412264699, 418997210078479016314891376985981834403, 310417325465458849274468827944195726858840449351291150876911355

Offset

1,3

Links

Table of n, a(n) for n=1..13.

Formula

a(n) tends towards a(n-1)^phi and 1.31809...^(phi^n) where phi=(1+sqrt(5))/2=1.6180339887...

a(n)=a(n-1)*a(n-2)+a(n-3)*a(n-1)+a(n-2)*a(n-3). - M. F. Hasler, Jan 01 2013

Example

a(6)=17*5*2*(1/17+1/5+1/2)=129.

Mathematica

nxt[{a_, b_, c_}]:={b, c, a*b*c*(1/a+1/b+1/c)}; NestList[nxt, {1, 1, 2}, 15][[;; , 1]] (* Harvey P. Dale, Jan 22 2026 *)

Crossrefs

Cf. A074047. In more than one sense A074046 comes between A000045 and A057438.

See also A121810 and A203761 and references therein.

Sequence in context: A174168 A097980 A210525 * A123374 A067339 A309178

Adjacent sequences: A074043 A074044 A074045 * A074047 A074048 A074049

Keyword

nonn

Author

Henry Bottomley, Aug 14 2002

Status

approved